Transcript
00:00:00 The following is a conversation with Stephen Wolfram, his third time on the podcast.
00:00:04 He’s a computer scientist, mathematician, theoretical physicist, and the founder of
00:00:10 Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the new
00:00:16 Wolfram Physics Project. This conversation is a wild technical roller coaster ride
00:00:22 through topics of complexity, mathematics, physics, computing, and consciousness.
00:00:28 I think this is what this podcast is becoming, a wild ride. Some episodes are about physics,
00:00:34 some about robots, some are about war and power, some are about the human condition
00:00:40 and our search for meaning, and some are just what the comedian Tim Dillon calls fun.
00:00:47 This is the Lex Friedman Podcast, to support it please check out the sponsors in the description,
00:00:52 and now here’s my conversation with Stephen Wolfram.
00:00:56 Stephen.
00:00:57 Almost 20 years ago, you published A New Kind of Science, where you presented a study of
00:01:03 complexity and an approach for modeling of complex systems. So, let us return again to
00:01:10 the core idea of complexity. What is complexity?
00:01:15 I don’t know, I think that’s not the most interesting question. It’s like,
00:01:19 you know, if you ask a biologist what is life, that’s not the question they care the most about.
00:01:24 But what I was interested in is, how does something that we would usually identify as
00:01:31 complexity arise in nature? And I got interested in that question like 50 years ago, which is
00:01:35 really embarrassingly long time ago. And, you know, I was, you know, how does snowflakes get
00:01:41 to have complicated forms? How do galaxies get to have complicated shapes? How do living systems
00:01:47 get produced? Things like that. And the question is, what’s the sort of underlying scientific
00:01:52 basis for those kinds of things? And the thing that I was at first very surprised by, because
00:01:57 I’ve been doing physics and particle physics, some fancy mathematical physics and so on.
00:02:02 And it’s like, I know all this fancy stuff, I should be able to solve this sort of basic
00:02:06 science question. And I couldn’t, this was like early, maybe 1980 ish timeframe. And it’s like,
00:02:13 okay, what can one do to understand the sort of basic secret that nature seems to have?
00:02:19 Because it seems like nature, you look around in the natural world, it’s full of incredibly
00:02:22 complicated forms. You look at sort of most engineered kinds of things, for instance,
00:02:28 they tend to be, you know, we’ve got sort of circles and lines and things like this.
00:02:34 And the question is, what secret does nature have that lets it make all this complexity
00:02:38 that we in doing engineering, for example, don’t naturally seem to have?
00:02:42 And so that was the kind of the thing that I got interested in. And then the question was,
00:02:46 you know, could I understand that with things like mathematical physics? Well, it didn’t work
00:02:51 very well. So then I got to thinking about, okay, is there some other way to try to understand this?
00:02:56 And then the question was, if you’re going to look at some system in nature,
00:03:00 how do you make a model for that system, for what that system does? So, you know,
00:03:03 a model is some abstract representation of the system, some formal representation system.
00:03:08 What is the raw material that you can make that model out of? And so what I realized was,
00:03:15 well, actually, programs are a really good source of raw material for making models of things.
00:03:20 And, you know, in terms of my personal history, to me, that seemed really obvious. And the reason
00:03:26 it seemed really obvious is because I just spent several years building this big piece of software
00:03:30 that was sort of a predecessor to Mathematica and Morphan Language, then called SMP, Symbolic
00:03:35 Manipulation Program, which was something that had this idea of starting from just these
00:03:41 computational primitives and building up everything one had to build up. And so kind of the notion of,
00:03:46 well, let’s just try and make models by starting from computational primitives and seeing what we
00:03:50 can build up, that seemed like a totally obvious thing to do. In retrospect, it might not have been
00:03:56 externally quite so obvious, but it was obvious to me at the time, given the path that I happened
00:04:00 to have been on. So, you know, so that got me into this question of, let’s use programs
00:04:06 to model what happens in nature. And the question then is, well, what kind of programs?
00:04:11 And, you know, we’re used to programs that you write for some particular purpose, and it’s a
00:04:15 big, long piece of code, and it does some specific thing. But what I got interested in was, okay,
00:04:20 if you just go out into the sort of computational universe of possible programs, you say,
00:04:25 take the simplest program you can imagine, what does it do? And so I started studying these things
00:04:30 called cellular automata. Actually, I didn’t know at first they were called cellular automata,
00:04:34 but I found that out subsequently. But it’s just a line of cells, you know, each one is black or
00:04:39 white, and it’s just some rule that says the color of the cell is determined by the color that it had
00:04:44 on the previous step and its two neighbors on the previous step. And I had initially thought,
00:04:50 that’s, you know, sufficiently simple setup is not going to do anything interesting. It’s always
00:04:55 going to be simple, no complexity, simple rule, simple behavior. Okay, but then I actually ran
00:05:00 the computer experiment, which was pretty easy to do. I mean, it probably took a few hours
00:05:05 originally. And the results were not what I’d expected at all. Now, needless to say,
00:05:12 in the way that science actually works, the results that I got had a lot of unexpected
00:05:16 things which I thought were really interesting, but the really strongest results, which was
00:05:21 already right there in the printouts I made, I didn’t really understand for a couple more years.
00:05:25 So it was not, you know, the compressed version of the story is you run the experiment and you
00:05:31 immediately see what’s going on, but I wasn’t smart enough to do that, so to speak. But the
00:05:36 big thing is, even with very simple rules of that type, sort of the minimal, tiniest program,
00:05:43 sort of the one line program or something, it’s possible to get very complicated behavior. My
00:05:49 favorite example is this thing called Rule 30, which is a particular cellular automaton rule.
00:05:54 You just started off from one black cell and it makes this really complicated pattern. And so that
00:06:00 for me was sort of a critical discovery that then kind of said, playing back onto, you know,
00:06:07 how does nature make complexity, I sort of realized that might be how it does it.
00:06:12 That might be kind of the secret that it’s using is that in this kind of computational
00:06:16 universe of possible programs, it’s actually pretty easy to get programs where even though
00:06:20 the program is simple, the behavior when you run the program is not simple at all.
00:06:24 And so for me, that was the kind of the story of kind of how that was sort of the indication that
00:06:33 one had got an idea of what the sort of secret that nature uses to make complexity and how
00:06:38 complexity can be made in other places. Now, if you say, what is complexity? You know,
00:06:46 complexity is it’s not easy to tell what’s going on. That’s the informal version of what is
00:06:52 complexity, but there is something going on, but there’s a rule to know what, right? Well, no,
00:06:57 the rules can generate just randomness, right? Well, that’s not obvious. In other words,
00:07:04 it’s not obvious at all. And it wasn’t what I expected. It’s not what people’s intuition
00:07:09 had been and has been for, you know, for a long time. That is one might think you have a rule.
00:07:15 You can tell there’s a rule behind it. I mean, it’s just like, you know, the early, you know,
00:07:20 robots in science fiction movies, right? You can tell it’s a robot cause it does simple things,
00:07:27 right? It turns out that isn’t actually the right story, but it’s not obvious that isn’t the right
00:07:31 story because people assume simple rules, simple behavior. And that the sort of the key discovery
00:07:37 about the computational universe is that isn’t true. And that discovery goes very deep and
00:07:43 relates to all kinds of things that I’ve spent years and years studying. But, you know, that in
00:07:48 the end, the sort of the, the what is complexity is, well, you can’t easily tell what it’s going
00:07:54 to do. You could just run the rule and see what happens, but you can’t just say, oh, you know,
00:08:00 show me the rule. Great. And now I know what’s going to happen. And, you know, the key phenomenon
00:08:04 around that is this thing I call computational irreducibility. This fact that in something like
00:08:11 rule 30, you might say, well, what’s it going to do after a million steps? Well, you can run it
00:08:16 for a million steps and just do what it does to find out, but you can’t compress that. You can’t
00:08:21 reduce that and say, I’m going to be able to jump ahead and say, this is what it’s going to do after
00:08:25 a million steps, but I don’t have to go through anything like that computational effort.
00:08:29 CB. By the way, has anybody succeeded at that? Do you have to challenge a competition
00:08:34 for predicting the middle column of rule 30? Anybody?
00:08:37 MG. A number of people have sent things in and sort of people are picking away at it,
00:08:41 but it’s hard. I mean, I’ve been actually even proving that the center column of rule 30 doesn’t
00:08:50 repeat. That’s something I think might be doable. Okay?
00:08:54 CB. Mathematically proving.
00:08:55 MG. Yes. And so that’s analogous to a similar kind of thing as like the digits of pi,
00:09:00 which are also generated in this very deterministic way. And so a question is how random are the
00:09:06 digits of pi? For example, first of all, do the digits of pi ever repeat? We know they don’t,
00:09:11 because it was proved in the 1800s that pi is not a rational number. So that means only rational
00:09:17 numbers have digit sequences that repeat. So we know the digits of pi don’t repeat.
00:09:21 So now the question is, does 0, 1, 2, 3 or whatever, do all the digits base 10 or base 2 or
00:09:27 however you work it out, do they all occur with equal frequency? Nobody knows. That’s far away
00:09:33 from what can be understood mathematically at this point. But I’m even looking for step one,
00:09:41 which is prove that the center column doesn’t repeat and then prove other things about it,
00:09:46 like equidistribution of equal numbers of zeros and ones. And those are things which I kind of
00:09:52 set up this little prize thing because I thought those were not too out of range. Those are things
00:09:59 which are within a modest amount of time, it’s conceivable that those could be done. They’re not
00:10:06 far away from what current mathematics might allow. They’ll require a bunch of cleverness
00:10:11 and hopefully some interesting new ideas that will be useful other places.
00:10:16 But you started in 1980 with this idea before I think you realized this idea of programs.
00:10:23 You thought that there might be some kind of a thermodynamic randomness and then complexity
00:10:29 comes from a clever filter that you kind of like, I don’t know, spaghetti or something. You filter
00:10:37 the randomness and outcomes complexity, which is an interesting intuition. How do we know that’s
00:10:43 not actually what’s happening? So just because you were then able to develop, look, you don’t need
00:10:50 this like incredible randomness. You can just have very simple, predictable initial conditions
00:10:56 and predictable rules. And then from that emerged complexity, still there might be some systems
00:11:02 where it’s filtering randomness on the inputs. Well, the point is when you have quotes randomness
00:11:11 in the input, that means there’s all kinds of information in the input. And in a sense,
00:11:15 what you get out will be maybe just something close to what you put in. Like people are very
00:11:21 in dynamical systems theory, sort of big area mathematics that developed
00:11:25 from the early 1900s and really got big in the 1980s. An example of what people study
00:11:31 there a lot and it’s popular version is chaos theory. An example of what people study a lot
00:11:37 is the shift map, which is basically taking 2x mod one to the fractional part of 2x,
00:11:44 which is basically just taking digits in binary and shifting them to the left. So at every step,
00:11:49 you get to see if you say, how big is this number that I got out? Well, the most important digit in
00:11:54 that number is whatever ended up at the left hand end. But now if you start off from an arbitrary
00:12:00 random number, which is quotes randomly chosen, so all its digits are random, then when you run
00:12:06 that sort of chaos theory shift map, all that you get out is just whatever you put in. You just get
00:12:12 to see what you… It’s not obvious that you would excavate all of those digits. And if you’re,
00:12:18 for example, making a theory, I don’t know, fluid mechanics, for example, if there was that
00:12:22 phenomenon in fluid mechanics, then the equations of fluid mechanics can’t be right. Because what
00:12:27 that would be saying is the equations that it matters to the fluid, what happens in the fluid
00:12:33 at the level of the millionth digit of the initial conditions, which is far below the point at which
00:12:40 you’re hitting sizes of molecules and things like that. So it’s kind of almost explaining
00:12:45 if that phenomenon is an important thing, it’s kind of telling you that fluid dynamics,
00:12:50 which describes fluids as continuous media and so on, isn’t really right.
00:12:54 But so this idea that… It’s a tricky thing because as soon as you put randomness in,
00:13:01 you have to know how much of what’s coming out is what you put in versus how much is actually
00:13:07 something that’s being generated. And what’s really nice about these systems where you just
00:13:11 have very simple initial conditions and where you get random stuff out or seemingly random stuff out
00:13:17 is you don’t have that issue. You don’t have to argue about, was there something complicated put
00:13:21 in? Because it’s plainly obvious there wasn’t. Now, as a practical matter in doing experiments,
00:13:26 the big thing is if the thing you see is complex and reproducible, then it didn’t come from just
00:13:34 filtering some, quotes, randomness from the outside world. It has to be something that is
00:13:39 intrinsically made because it wouldn’t otherwise be… It could be the case that you set things up
00:13:45 and it’s always the same each time and you say, well, it’s kind of the same, but it’s not random
00:13:51 each time because it’s kind of the definition of it being random is it was kind of picked at random
00:13:57 each time, so to speak. So is it possible to for sure know that our universe does not at the
00:14:03 fundamental level have randomness? Is it possible to conclusively say there’s no randomness at the
00:14:10 bottom? Well, it’s an interesting question. I mean, you know, science, natural science is an
00:14:16 inductive business, right? You observe a bunch of things and you say, can we fit these together?
00:14:21 What is our hypothesis for what’s going on? The thing that I think I can say fairly definitively
00:14:27 is at this point, we understand enough about fundamental physics that if there was sort of
00:14:34 an extra dice being thrown, it’s something that doesn’t need to be there. We can get what we see
00:14:41 without that. Now, could you add that in as an extra little featureoid without breaking the
00:14:49 universe? Probably, but in fact, almost certainly yes. But is it necessary for understanding the
00:14:56 universe? No. And I think actually from a more fundamental point of view, I think I might be
00:15:03 able to argue. So one of the things that I’ve been interested in and been pretty surprised that I’ve
00:15:07 had anything sentient to say about is the question of why does the universe exist? I didn’t think
00:15:13 that was a question that I would, you know, I thought that was a far out there metaphysical
00:15:18 kind of thing. Even the philosophers have stayed away from that question for the most part.
00:15:23 It’s such a kind of difficult to address question. But I actually think to my great surprise that
00:15:30 from our physics project and so on, that it is possible to actually address that question and
00:15:36 explain why the universe exists. And I kind of have a suspicion. I’ve not thought it through.
00:15:40 I kind of have a suspicion that that explanation will eventually show you that in no meaningful
00:15:46 sense can there be randomness underneath the universe. That is that if there is, it’s something
00:15:52 that is necessarily irrelevant to our perception of the universe. That is that it could be there,
00:15:59 but doesn’t matter because in a sense, we’ve already, you know, whatever it would do,
00:16:04 whatever extra thing it would add is not relevant to our perception of what’s going on.
00:16:09 So why does the universe exist? How does the relevance of randomness connect to the big
00:16:17 why question of the universe? So, OK, so I mean, why does the universe exist? Well, let’s see.
00:16:23 And is this the only universe we got? It’s the only one that about that I’m pretty sure.
00:16:28 So now maybe which one which of these topics is better to enter first? Why does the universe exist
00:16:35 and why you think it’s the only one that exists? Well, I think they’re very closely related. OK.
00:16:41 OK. So, I mean, the first thing, let’s see, I mean, this why does the universe exist question
00:16:47 is built on top of all these things that we’ve been figuring out about fundamental physics,
00:16:52 because if you want to know why the universe exists, you kind of have to know what the
00:16:55 universe is made of. And I think the well, let me let me describe a little bit about
00:17:02 the why does the universe exist question. So the main issue is let’s say you have a model
00:17:07 for the universe and you say I’ve got this this program or something and you run it and you make
00:17:12 the universe. Now you say, well, how do you actually why is that program actually running?
00:17:17 And people say you’ve got this program that makes the universe. What computer is it running on?
00:17:21 Right. What what does it mean? What actualizes something? You know, two plus two equals four.
00:17:27 But that’s different from saying this to a pile of two rocks, another pile of two rocks, and so
00:17:31 many moves them together and makes four, so to speak. And so what is it that kind of turns it
00:17:37 from being just this formal thing to being something that is actualized? OK, so there we
00:17:43 have to start thinking about, well, well, what do we actually know about what’s going on in the
00:17:47 universe? Well, we are observers of this universe. But confusingly enough, we’re part of this
00:17:53 universe. So in a sense, we what what what if we say what do we what do we know about what’s
00:17:59 going on in the universe? Well, what we know is what sort of our consciousness records about
00:18:04 what’s going on in the universe. And consciousness is part of the fabric of the universe. So we’re
00:18:09 in it. Yes, we’re in it. And maybe I should maybe I should start off by saying something about
00:18:15 the consciousness story, because that’s some. Maybe we should begin even before that at the
00:18:23 very base layer of the Wolfram physics project. Maybe you can give a broad overview once again
00:18:29 really quick about this hypergraph model. Yes. And also, what is it a year and a half ago since
00:18:36 you’ve brought this project to the world? What is the status update where what are all the beautiful
00:18:42 ideas you have come across? What are the interesting things you can mention? It’s I mean,
00:18:48 it’s a it’s a frigging Cambrian explosion. I mean, it’s it’s crazy. I mean, there are all these
00:18:53 things which I’ve kind of wondered about for years. And suddenly, there’s actually a way to
00:18:58 think about them. And I really did not see. I mean, the real strength of what’s happened,
00:19:04 I absolutely did not see coming. And the real strength of it is we’ve got this model for physics,
00:19:09 but it turns out it’s a foundational kind of model. That’s a different kind of computation
00:19:13 like model that I’m kind of calling the sort of multi computational model. And that that kind of
00:19:20 model is applicable not only to physics, but also to lots of other kinds of things. And one reason
00:19:26 that’s extremely powerful is because physics has been very successful. So we know a lot based on
00:19:31 what we figured out in physics. And if we know that the same model governs physics and governs,
00:19:37 I don’t know, economics, linguistics, immunology, whatever, we know that the same kind of model
00:19:42 governs those things. We can start using things that we’ve successfully discovered in physics
00:19:47 and applying those intuitions in all these other areas. And that’s that’s pretty exciting and very
00:19:52 and very surprising to me. And in fact, it’s kind of like in the original story of sort of you go
00:19:59 and you explain why is there complexity in the natural world, then you realize, well, there’s all
00:20:03 this complexity, there’s all this computational irreducibility. You know, there’s a lot we can’t
00:20:08 know about what’s going to happen. It’s kind of kind of very confusing thing for people who say,
00:20:12 you know, science has nailed everything down. We’re going to, you know, based on science,
00:20:16 we can know everything. Well, actually, there’s this computational irreducibility thing
00:20:20 right in the middle of that, thrown up by science, so to speak. And then the question is, well,
00:20:25 given computational irreducibility, how can we actually figure out anything about what happens
00:20:29 in the world? Why aren’t we why are we able to predict anything? Why are we able to operate in
00:20:33 the world? And the answer is that we sort of live in these slices of computational reusability
00:20:39 that exist in this kind of ocean of computational irreducibility. And it turns out that seems that
00:20:45 it’s a very fundamental feature of the kind of model that seems to operate in physics,
00:20:50 and perhaps in a lot of these other areas, that there are these particular slices of
00:20:55 computational reusability that are relevant to us. And those are the things that both allow us to
00:21:02 operate in the world, and not just have everything be completely unpredictable. But there are also
00:21:06 things that potentially give us what amount to sort of physics like laws in all these other areas.
00:21:12 So that’s, that’s been sort of an exciting thing. But, but I would say that in general, for our
00:21:17 project, it’s been going spectacularly well. I mean, you know, I, it’s very, honestly, it wasn’t
00:21:23 something I expected to happen in my lifetime. I mean, it’s, you know, it’s something where,
00:21:28 where it’s, it’s an in fact, one of the things about it, some of the things that we’ve discovered,
00:21:34 are things where I was pretty sure that wasn’t how things worked. And turns out I’m wrong. And,
00:21:40 you know, in a major area in metamathematics, I’ve been realizing that I something I’ve long
00:21:45 believed we can talk about it later that that that just just really isn’t right. But But I think that
00:21:53 the the thing that so so what’s happened with the physics project? I mean, you know, it’s a
00:21:59 can explain a little bit about how the how the model works. But basically,
00:22:02 we can maybe ask you the following question. So it’s easy through words describe how cellular
00:22:08 automata works, you’ve you’ve explained this. And it’s the fundamental mechanism by which you in
00:22:16 your book, and you kind of science explored the idea of complexity and how to do science in this
00:22:21 world of island reducible islands and irreducible general irreducibility. Okay, so how does the model
00:22:30 of hypergraphs differ from cellular automata? And how does the idea of multi computation
00:22:35 differ? Like, maybe that’s a way to describe it. We’re we’re, you know, right. This is a, you know,
00:22:42 my life is like all of our lives, something of a story of computational irreducibility. Yes.
00:22:47 And, you know, it’s been going for a few years now. So it’s always a challenge to kind of find
00:22:52 these appropriate pockets of reducibility. But let me see what I can do. So, so I mean,
00:22:57 first of all, let’s let’s talk about physics, first of all. And, you know, a key observation,
00:23:03 that one of the starting point of our physics project is things about what is space? What is
00:23:09 the universe made of? And, you know, ever since Euclid, people just sort of say space is just this
00:23:15 thing where you can put things at any position you want. And they’re just points. And they’re just
00:23:19 geometrical things that you can just arbitrarily put at different different coordinate positions.
00:23:25 So the first thing in our physics project is the idea that space is made of something, just like
00:23:30 just like water is made of molecules, space is made of kind of atoms of space. And the only thing we
00:23:36 can say about these atoms of space is they have some identity. There’s a there’s a there is it’s
00:23:40 this atom as opposed to this atom. And, you know, you could give them a few a computer person, you
00:23:45 give them UUIDs or something. And that’s all there is to say about them, so to speak. And then all we
00:23:54 know about these atoms of space is how they relate to each other. So we say, these three atoms of
00:24:02 space are associated with each other in some relation. So you can think about that as you know,
00:24:08 what atom of space is friends with what other atom of space, you can build this essentially friend
00:24:13 network of the atoms of space. And the sort of starting point of our physics project is that’s
00:24:18 what our universe is, it’s a giant friend network of the atoms of space. And so how can that
00:24:24 possibly represent our universe? Well, it’s like in something like water, you know, their molecules
00:24:31 bouncing around, but on a large scale that, you know, that produces fluid flow, and we have fluid
00:24:37 vortices, and we have all of these phenomena that are sort of the emergent phenomena from that
00:24:42 underlying kind of collection of molecules bouncing around. And by the way, it’s important that that
00:24:47 collection of molecules bouncing around have this phenomenon of computational irreducibility,
00:24:51 that’s actually what leads to the second law of thermodynamics among other things.
00:24:55 And that leads to the sort of randomness of the underlying behavior, which is what gives you
00:25:00 something which on a large scale seems like it’s a smooth continuous type of thing. And so okay,
00:25:07 so first thing is space is made of something, it’s made of all these atoms of space connected
00:25:13 together in this network. And then everything that we experience is sort of features of that
00:25:20 structure of space. So, you know, when we have an electron or something or a photon,
00:25:24 it’s some kind of tangle in the structure of space, much like kind of a vortex in a fluid
00:25:29 would be just this thing that is, you know, it can actually, the vortex can move around,
00:25:34 it can involve different molecules in the fluid, but the vortex still stays there.
00:25:38 And if you zoom out enough, the vortex looks like an atom itself, like a basic
00:25:42 element. So there’s the levels of abstraction. If you squint and kind of blur things out,
00:25:49 it looks like at every level of abstraction, you can define what is a basic individual entity.
00:25:55 Yes. But, you know, in this model, there’s a bottom level, you know, there’s an elementary
00:26:01 length, maybe 10 to the minus 100 meters, let’s say, which is really small, you know,
00:26:05 proton is 10 to the minus 15 meters, the smallest we’ve ever been able to sort of see with a particle
00:26:12 accelerator is around 10 to the minus 21 meters. So, you know, if we don’t know precisely what
00:26:17 the correct scale is, but it’s perhaps over the order of 10 to the minus 100 meters, so it’s
00:26:21 pretty small. But that’s the end, that’s what things are made of.
00:26:26 What’s your intuition where the 10 to the minus 100 comes from? What’s your intuition about this
00:26:32 scale?
00:26:33 Well, okay, so there’s a calculation, which I consider to be somewhat rickety,
00:26:37 okay, which has to do with comparing, so there are various fundamental constants,
00:26:42 there’s a speed of light, the speed of light, once you know the elementary time,
00:26:46 the speed of light tells you the conversion from the elementary time to the elementary length.
00:26:52 Then there’s the question of how do you convert to the elementary energy? And how do you convert
00:26:56 to between other things? And the various constants we know, we know the speed of light,
00:27:00 we know the gravitational constant, we know Planck’s constant and quantum mechanics,
00:27:05 those are the three important ones. And we actually know some other things, we know things
00:27:09 like the size of the universe, the Hubble constant, things like that. And essentially,
00:27:15 this calculation of the elementary length comes from looking at the combination of those.
00:27:21 Okay, so the most obvious thing, people have assumed that quantum gravity happens at this
00:27:26 thing, the Planck scale, 10 to the minus 34 meters, which is the combination of Planck’s
00:27:32 constant and the gravitational constant, the speed of light, that gives you that kind of length.
00:27:37 Turns out in our model, there is an additional parameter, which is essentially the number of
00:27:42 simultaneous threads of execution of the universe, which is essentially the number of sort of
00:27:47 independent quantum processes that are going on. And that number, let’s see if I remember that
00:27:52 number, that number is 10 to the 170, I think, and so it’s a big number. But that number then
00:28:00 connects, sort of modifies what you might think from all these Planck units to give you the things
00:28:07 we’re giving. And there’s been sort of a mystery actually in the more technical physics thing,
00:28:12 that the Planck mass, the Planck energy, Planck energy is actually surprisingly big. The Planck
00:28:19 length is tiny, 10 to the minus 34 meters, you know, Planck time, 10 to the minus 43 meters,
00:28:24 I think, seconds, I think. But the Planck energy is like the energy of a lightning strike,
00:28:32 okay, which is pretty weird. In our models, the actual elementary energy is that divided by the
00:28:38 number of sort of simultaneous quantum threads, and it ends up being really small too. And that
00:28:43 sort of explains that mystery that’s been around for a while about how Planck units work. But
00:28:50 whether that precise estimate is right, we don’t know yet. I mean, that’s one of the things that’s
00:28:54 sort of been a thing we’ve been pretty interested in is how do you see through, you know, how do you
00:29:00 make a gravitational microscope that can kind of see through to the atoms of space? You know,
00:29:05 how do you get in fluid flow, for example, if you go to hypersonic flow or something, you know,
00:29:10 you’ve got a Mach 20, you know, space plane or something, it really matters that there are
00:29:15 individual molecules hitting the space plane, not a continuous fluid. The question is, what is the
00:29:22 analog of hypersonic flow for things about the structure of spacetime? And it looks like a
00:29:30 rapidly rotating black hole, right, at the sort of critical rotation rate, it looks as if that’s
00:29:38 a case where essentially the structure of spacetime is just about to fall apart, and you
00:29:45 may be able to kind of see the evidence of sort of discrete elements, you know, you may be able
00:29:52 to kind of see there the sort of gravitational microscope of actually seeing these discrete
00:29:57 elements of space. And there may be some effect in, for example, gravitational waves produced by
00:30:03 rapidly rotating black hole that in which one could actually see some phenomenon where one
00:30:08 can say, yes, these don’t come out the way one would expect based on having a continuous structure
00:30:14 of spacetime, that is something where you can kind of see through to the discrete structure.
00:30:19 We don’t know that yet. So can you maybe elaborate a little bit deeper how a microscope that can see
00:30:25 the 10 to the minus 100, how rotating black holes and presumably the detailed accurate
00:30:36 detection of gravitational waves from such black holes can reveal the discreteness of space?
00:30:42 Okay, first thing is, what is a black hole? Actually, we need to go a little bit further in
00:30:47 the story of what spacetime is, because I explained a little bit about what space is,
00:30:50 but I didn’t talk about what time is. And that’s sort of important in understanding spacetime,
00:30:55 so to speak. And your sense is both space and time in the story are discrete.
00:30:59 Absolutely. Absolutely. But it’s a complicated story. And needless to say.
00:31:05 Well, it’s simple at the bottom. It’s very simple at the bottom. In the end,
00:31:11 it’s simple but deeply abstract. And something that is simple in conception,
00:31:18 but kind of wrapping one’s head around what’s going on is pretty hard. So first of all,
00:31:24 we have this. So I’ve described these kind of atoms of space and their connections.
00:31:29 You can think about these things as a hypergraph. A graph is just you connect nodes to nodes,
00:31:34 but a hypergraph you can have not just individual friends to friends, but you can have these
00:31:40 triplets of friends or whatever else. And so we’re just saying that’s just the relations
00:31:47 between atoms of space are the hyperedges of the hypergraph. And so we got some big collection of
00:31:52 these atoms of space, maybe 10 to the 400 or something in our universe. And that’s the structure
00:31:59 of space. And every feature of what we experience in the world is a feature of that hypergraph,
00:32:07 that spatial hypergraph. So then the question is, well, what does that spatial hypergraph do?
00:32:12 Well, the idea is that there are rules that update that spatial hypergraph. And in a cellular
00:32:18 automaton, you’ve just got this line of cells and you just say at every step, at every time step,
00:32:23 you’ve got fixed time steps, fixed array of cells. At every step, every cell gets updated
00:32:29 according to a certain rule. And that’s the way it works. Now in this hypergraph, it’s sort of
00:32:36 vaguely the same kind of thing. We say every time you see a little piece of hypergraph that looks
00:32:40 like this, update it to one that looks like this. So just keep rewriting this hypergraph. Every time
00:32:47 you see something that looks like that, anywhere in the universe, it gets rewritten. Now, one thing
00:32:51 that’s tricky about that, which we’ll come to, is this multi computational idea, which has to do
00:32:56 with you’re not saying in some kind of lockstep way, do this one, then this one, then this one.
00:33:02 It’s just whenever you see one you can do, you can go ahead and do it. And that leads one not to
00:33:07 have a single thread of time in the universe. Because if you knew which one to do, you just say,
00:33:13 okay, we do this one, then we do this one, then we do this one. But if you say, just do whichever
00:33:17 one you feel like, you end up with these multiple threads of time, these kind of multiple histories
00:33:21 of the universe, depending on which order you happen to do the things you could do in.
00:33:26 So it’s fundamentally asynchronous and parallel.
00:33:28 Yes. Yes.
00:33:30 Which is very uncomfortable for the human brain that seeks for things to be sequential.
00:33:35 Yes.
00:33:35 And synchronous.
00:33:36 Right. Well, I think that this is part of the story of consciousness,
00:33:42 is I think the key aspect of consciousness that is important for sort of parsing the universe,
00:33:48 is this point that we have a single thread of experience. We have a memory of what happened
00:33:53 in the past. We can say something, predict something about the future, but there’s a single
00:33:57 thread of experience. And it’s not obvious it should work that way. I mean, we’ve got 100
00:34:00 billion neurons in our brains and they’re all firing at all kinds of different ways.
00:34:04 But yet, our experience is that there is the single thread of time that goes along. And I
00:34:12 think that one of the things I’ve kind of realized with a lot more clarity in the last year is the
00:34:18 fact that the fact that we conclude that the universe has the laws it has is a consequence
00:34:24 of the fact that we have consciousness the way we have consciousness. And so, just to go on with
00:34:31 kind of the basic setup, so we’ve got this spatial hypergraph, it’s got all these atoms of space,
00:34:38 they’re getting these little clumps of atoms of space, they’re getting turned into other clumps
00:34:41 of atoms of space, and that’s happening everywhere in the universe all the time. And so, one thing
00:34:45 that’s a little bit weird is there’s nothing permanent in the universe. The universe is getting
00:34:49 rewritten everywhere all the time. And if it wasn’t getting rewritten, space wouldn’t be knitted
00:34:53 together. That is, space would just fall apart. There wouldn’t be any way in which we could say
00:34:58 this part of space is next to this part of space. One of the things that people were confused about
00:35:04 back in antiquity, the ancient Greek philosophers and so on, is how does motion work? How can it be
00:35:11 the case that you can take a thing that we can walk around and it’s still us when we walked a
00:35:16 foot forward, so to speak? And in a sense, with our models, that’s again a question because it’s
00:35:23 a different set of atoms of space. When I move my hand, it’s moving into a different set of atoms
00:35:29 of space. It’s having to be recreated. The thing itself is not there. It’s being continuously
00:35:35 recreated all the time. Now, it’s a little bit like waves in an ocean, vortices in a fluid,
00:35:40 which again, the actual molecules that exist in those are not what define the identity of the
00:35:46 thing. But this idea that there can be pure motion, that it is even possible for an object
00:35:55 to just move around in the universe and not change, it’s not self evident that such a thing
00:36:00 should be possible. And that is part of our perception of the universe is that we parse
00:36:06 those aspects of the universe where things like pure motion are possible. Now, pure motion,
00:36:11 even in general relativity, the theory of gravity, pure motion is a little bit of a complicated
00:36:16 thing. I mean, if you imagine your average teacup or something approaching a black hole,
00:36:21 it is deformed and distorted by the structure of space time. And to say, is it really pure motion?
00:36:27 Is it that same teacup that’s the same shape? Well, it’s a bit of a complicated story. And this
00:36:32 is a more extreme version of that. So anyway, the thing that’s happening is we’ve got space,
00:36:38 we’ve got this notion of time. So time is this kind of this rewriting of the hypergraph. And one
00:36:45 of the things that’s important about that time is this sort of computational irreducible process.
00:36:50 There’s something, you know, time is not something where it’s kind of the mathematical view of time
00:36:56 tends to be time is just to coordinate. We can, you know, slide a slider, turn a knob,
00:37:01 and we’ll change the time that we’ve got in this equation. But in this picture of time,
00:37:06 that’s not how it works at all. Time is this inexorable, irreducible kind of set of computations
00:37:12 that go on, that go from where we are now to the future. And one of the things that is, again,
00:37:20 something one sort of has to break out of is your average trained physicist like me says,
00:37:25 you know, space and time are the same kind of thing. They’re related by, you know,
00:37:29 the Poincare group and Lorentz transformations and relativity and all these kinds of things.
00:37:34 And, you know, space and time, you know, there are all these kind of sort of folk stories you
00:37:38 can tell about why space and time are the same kind of thing. In this model, they’re fundamentally
00:37:43 not the same kind of thing. Space is this kind of sort of connections between these atoms of space.
00:37:49 Time is this computational process. So the thing that the first sort of surprising thing is, well,
00:37:55 it turns out you get relativity anyway. And the reason that happens, there are a few bits and
00:38:00 pieces here which one has to understand. But the fundamental point is if you are an observer
00:38:06 embedded in the system that are part of this whole story of things getting updated in this way and
00:38:12 that, there’s sort of a limit to what you can tell about what’s going on. And really, in the end,
00:38:18 the only thing you can tell is what are the causal relationships between events. So an event in this
00:38:24 sort of an elementary event is a little piece of hypergraph got rewritten. And that means a few
00:38:31 hyper edges of the hypergraph were consumed by the event and you produce some other hyper edges.
00:38:36 And that’s an elementary event. And so then the question is what we can tell is kind of what the
00:38:43 network of causal relationships between elementary events is. That’s the ultimate thing,
00:38:48 the causal graph of the universe. And it turns out that, well, there’s this property of causal
00:38:53 invariance that is true of a bunch of these models and I think is inevitably true for a variety of
00:38:59 reasons that makes it be the case that it doesn’t matter kind of if you are sort of saying, well,
00:39:08 I’ve got this hypergraph and I can rewrite this piece here and this piece here and I do them all
00:39:12 in different orders. When you construct the causal graph for each of those orders that you choose to
00:39:17 do things in, you’ll end up with the same causal graph. And so that’s essentially why, well,
00:39:24 that’s in the end why relativity works. It’s why our perception of space and time is as having
00:39:31 this kind of connection that relativity says they should have. And that’s kind of how that works.
00:39:37 I think I’m missing a little piece. If we can go there again, you said the fact that the
00:39:42 observer is embedded in this hypergraph, what’s missing? What is the observer not able to state
00:39:50 about this universe of space and time? If you look from the outside, you can say,
00:39:55 oh, I see this particular place was updated and then this one was updated and I’m seeing which
00:40:05 order things were updated in. But the observer embedded in the universe doesn’t know which order
00:40:09 things were updated in because until they’ve been updated, they have no idea what else happened.
00:40:14 So the only thing they know is the set of causal relationships. Let me give an extreme example.
00:40:20 Let’s imagine that the universe is a Turing machine. Turing machines have just this one
00:40:25 update head which does something and otherwise the Turing machine just does nothing.
00:40:30 And the Turing machine works by having this head move around and do its updating just where the
00:40:35 head happens to be. The question is, could the universe be a Turing machine? Could the universe
00:40:40 just have a single updating head that’s just zipping around all over the place? You say,
00:40:44 that’s crazy because I’m talking to you, you seem to be updating, I’m updating,
00:40:49 et cetera. But the thing is, there’s no way to know that because if there was just this head
00:40:53 moving around, it’s like, okay, it updates me, but you’re completely frozen at that point.
00:40:58 Until the head has come over and updated you, you have no idea what happened to me.
00:41:02 And so if you sort of unravel that argument, you realize the only thing we actually can tell
00:41:07 is what the network of causal relationships between the things that happened were. We don’t
00:41:13 get to know from some sort of outside, sort of God’s eye view of the thing. We don’t get to know
00:41:19 what sort of from the outside, what happened. We only get to know sort of what the set of
00:41:26 relationships between the things that happened actually were.
00:41:28 Yeah. But if I somehow record like a trace of this, I guess it would be called multi computation.
00:41:36 Can’t I then look back in the causal tree?
00:41:40 Where do you record the trace?
00:41:42 Some, you place throughout the universe, like throughout like a log that records in my own
00:41:50 pocket of, in this hypergraph. Can’t I, like realizing that I’m getting an outdated picture,
00:41:56 can’t I record?
00:41:58 See, the problem is, and this is where things start getting very entangled in terms of what
00:42:03 one understands. The problem is that any such recording device is itself part of the universe.
00:42:10 Yeah.
00:42:10 So you don’t get to say, you never get to say, let’s go outside the universe and go do this.
00:42:16 And that’s why, I mean, lots of the features of this model and the way things work end up being
00:42:22 a result of that.
00:42:23 So, but what, I guess from on a human level, what is the cost you’re paying? What are you missing
00:42:30 from not getting an updated picture all the time? Okay. I got, I understand what you’re saying.
00:42:34 Yeah, yeah, right.
00:42:35 But like what, like, how does consciousness emerge from that? Like how, like, what are
00:42:41 the limitations of that observer? I understand you’re getting a delayed picture.
00:42:45 Well, there’s, there’s a, okay. So there’s, there’s a bunch of limitations of the observer, I think.
00:42:50 Yeah. Maybe just explain something about quantum mechanics, because that maybe is a,
00:42:54 is an extreme version of some of these issues, which helps to kind of motivate why one should
00:42:59 sort of think things through a little bit more carefully. So one feature of the, of this, okay.
00:43:05 So in standard physics, like high school physics, you learn, you know, the equations of motion for
00:43:10 a ball and the, the, you know, it says you throw the ball this angle, this velocity,
00:43:16 things will move in this way. And there’s a definite answer, right? The story, the key story
00:43:21 of quantum mechanics is there aren’t definite answers to where does the ball go? There’s kind
00:43:25 of this whole sort of bundle of possible paths. And all we say we know from quantum mechanics
00:43:32 is certain probabilities for where the ball will end up. Okay. So that’s kind of the,
00:43:36 the core idea of quantum mechanics. So in our models, you, quantum mechanics is not some kind
00:43:42 of plugin add on type thing. You absolutely cannot get away from quantum mechanics because
00:43:47 as you think about updating this hypergraph, there isn’t just one sequence of things,
00:43:51 one definite sequence of things that can happen. There are all these different possible update
00:43:55 sequences that can occur. You could do this, you know, piece of the hypergraph now, and then this
00:43:59 one later and et cetera, et cetera, et cetera. All those different paths of history correspond to
00:44:05 these quantum, quantum paths and quantum mechanics, these different possible quantum histories.
00:44:10 And one of the things that’s kind of surprising about it is they, they branch, you know, there can
00:44:15 be a certain state of the universe and it could do this or it could do that, but they can also
00:44:20 merge. There can be two states of the universe, which their next state, the next state they
00:44:25 produce is the same for both of them. And that process of branching and merging is kind of
00:44:30 critical. And the idea that there can be merging is critical and somewhat non trivial for these
00:44:34 hypergraphs because there’s a whole graph isomorphism story and there’s a whole very
00:44:39 elaborate set of mathematics. Yes. Among other things. Right. Yes. But so then what happens is
00:44:47 that what one’s seeing, okay, so we’ve got this thing, it’s branching, it’s merging, et cetera,
00:44:53 et cetera, et cetera. Okay. So now the question is how do we perceive that? Why don’t we notice
00:45:01 that the universe is branching and merging? Why is it the case that we just think a definite set
00:45:06 of things happen? Well, the answer is we are embedded in that universe and our brains are
00:45:11 branching and merging too. And so what quantum mechanics becomes a story of is how does a
00:45:16 branching brain perceive a branching universe? And the key thing is as soon as you say,
00:45:23 I think definite things happen in the universe, that means you are essentially conflating
00:45:28 lots of different parts of history. You’re saying, actually, as far as I’m concerned,
00:45:33 because I’m convinced that definite things happen in the universe, all these parts of history must
00:45:38 be equivalent. Now, it’s not obvious that that would be a consistent thing to do. It might be,
00:45:42 you say, all these parts of history are equivalent, but by golly, moments later,
00:45:47 that would be a completely inconsistent point of view. Everything would have gone to hell in
00:45:51 different ways. The fact that that doesn’t happen is, well, that’s a consequence of this causal
00:45:56 invariance thing. And the fact that that does happen a little bit is what causes little quantum
00:46:01 effects. And if that didn’t happen at all, there wouldn’t be anything that sort of is like quantum
00:46:08 mechanics. Quantum mechanics is kind of like in this bundle of paths. It’s a little bit like what
00:46:16 happens in statistical mechanics and fluid mechanics, whatever, that most of the time,
00:46:20 you just see this continuous fluid. You just see the world just progressing in this kind of way
00:46:25 that’s like this continuous fluid. But every so often, if you look at the exact right experiment,
00:46:29 you can start seeing, well, actually, it’s made of these molecules where they might go that way,
00:46:33 or they might go this way, and that’s kind of quantum effects. And so, this kind of idea of
00:46:41 where we’re sort of embedded in the universe, this branching brain is perceiving this branching
00:46:45 universe, and that ends up being sort of a story of quantum mechanics. That’s part of the whole
00:46:51 picture of what’s going on. But I think, I mean, to come back to sort of what is the story of
00:46:56 consciousness. So, in the universe, we’ve got whatever it is, 10 to the 400 atoms of space,
00:47:03 they’re all doing these complicated things. It’s all a big, complicated, irreducible computation.
00:47:08 The question is, what do we perceive from all of that? And the answer is that we are parsing the
00:47:15 universe in a particular way. Let me again go back to the gas molecules analogy. In the gas in this
00:47:23 room, there are molecules bouncing around all kinds of complicated patterns, but we don’t care.
00:47:28 All we notice is there’s, you know, the gas laws are satisfied. Maybe there’s some fluid dynamics.
00:47:34 These are kind of features of that assembly of molecules that we notice, and then lots of details
00:47:40 we don’t notice. When you say we, do you mean the tools of physics, or do you mean literally
00:47:44 the human brain and its perception system? Well, okay. So, the human brain is where it starts,
00:47:50 but we’ve built a bunch of instruments to do a bit better than the human brain, but they still
00:47:53 have many of the same kinds of ideas, you know, their cameras and their pressure sensors and
00:47:58 these kinds of things. They’re not, you know, at this point, we don’t know how to make
00:48:04 fundamentally qualitatively different sensory devices. Right. So, it’s always just an extension
00:48:09 of the consciousness experience. Or our sensory experience. Sensory experience, but
00:48:14 sensory experience is somehow intricately tied to consciousness. Right. Well, so one question is,
00:48:20 when we are looking at all these molecules in the gas, and there might be 10 to the 20th molecules
00:48:24 in some little box or something, it’s like, what do we notice about those molecules? So,
00:48:30 one thing that we can say is, we don’t notice that much. We are, you know, we are computationally
00:48:36 bounded observers. We can’t go in and say, okay, I’m the 10 to the 20th molecules, and I know
00:48:43 that I can sort of decrypt their motions, and I can figure out this and that. It’s like, I’m just
00:48:47 going to say, what’s the average density of molecules? And so, one key feature of us is that
00:48:52 we are computationally bounded. And that when you are looking at a universe which is full of
00:48:57 computation and doing huge amounts of computation, but we are computationally bounded, there’s only
00:49:03 certain things about that universe that we’re going to be sensitive to. We’re not going to be,
00:49:08 you know, figuring out what all the atoms of space are doing, because we’re just computationally
00:49:13 bounded observers, and we are only sampling these small set of features. So, I think the
00:49:19 two defining features of consciousness that, and I, you know, I would say that the sort of the
00:49:25 preamble to this is, for years, you know, as I’ve talked about sort of computation and fundamental
00:49:30 features of physics and science, people ask me, so what about consciousness? And I, for years,
00:49:36 I’ve said, I have nothing to say about consciousness. And, you know, I’ve kind of
00:49:40 told this story, you know, you talk about intelligence, you talk about life. These are
00:49:45 both features where you say, what’s the abstract definition of life? We don’t really know the
00:49:49 abstract definition. We know the one for life on Earth, it’s got RNA, it’s got cell membranes,
00:49:53 it’s got all this kind of stuff. Similarly for intelligence, we know the human definition of
00:49:58 intelligence, but what is intelligence abstractly? We don’t really know. And so, what I’ve long
00:50:03 believed is that sort of the abstract definition of intelligence is just computational sophistication.
00:50:09 That is, that as soon as you can be computationally sophisticated, that’s kind of the abstract
00:50:14 version, the generalized version of intelligence. So, then the question is, what about consciousness?
00:50:20 And what I sort of realized is that consciousness is actually a step down from intelligence. That
00:50:26 is, that you might think, oh, you know, consciousness is the top of the pie, but it’s
00:50:32 the top of the pile. But actually, I don’t think it is. I think that there’s this notion of kind
00:50:37 of computational sophistication, which is the generalized intelligence. But consciousness
00:50:42 has two limitations, I think. One of them is computational boundedness. That is, that we’re
00:50:47 only perceiving a sort of computationally bounded view of the universe. And the other is this idea
00:50:53 of a single thread of time. That is, that we, and in fact, we know neurophysiologically our brains
00:50:59 go to some trouble to give us this one thread of attention, so to speak. And it isn’t the case that
00:51:05 in all the neurons in our brains that, at least in our conscious, the correspondence of language,
00:51:12 in our conscious experience, we just have the single thread of attention, single thread of
00:51:17 perception. And maybe there’s something unconscious that’s bubbling around that’s the kind of
00:51:23 almost the quantum version of what’s happening in our brain, so to speak. We’ve got the classical
00:51:28 flow of what we are mostly thinking about, so to speak. But there’s this kind of bubbling around
00:51:33 of other paths that is all those other neurons that didn’t make it to be part of our sort of
00:51:38 conscious stream of experience. So in that sense, intelligence as computational sophistication is
00:51:44 much broader than the computational constraints which consciousness operates under, and also the
00:51:54 sequential, like the sequential thing, like the notion of time. That’s kind of interesting. But
00:51:59 then the follow up question is like, okay, starting to get a sense of what is intelligence, and how
00:52:05 does that connect to our human brain? Because you’re saying intelligence is almost like a fabric,
00:52:12 like what we like plug into it or something, like our consciousness plugs into it.
00:52:18 Yeah, I mean, the intelligence, I think the core, I mean, you know, intelligence at some
00:52:23 level is just a word, but we are asking, you know, what is the notion of intelligence as we
00:52:28 generalize it beyond the bounds of humans, beyond the bounds of even the AIs that we humans have
00:52:33 built and so on? You know, what is intelligence? You know, is the weather, you know, people say the
00:52:39 weather has a mind of its own. What does that mean? You know, can the weather be intelligent?
00:52:43 Yeah. What does agency have to do with intelligence here? So is intelligence just
00:52:48 like your conception of computation, just intelligence is the capacity to perform
00:52:54 computation and the sea of? Yeah, I think so. I mean, I think that’s right. And I think that,
00:52:59 you know, this question of, is it for a purpose? Okay, that quickly degenerates into a horrible
00:53:07 philosophical mess. Because, you know, whenever you say, did the weather do that for a purpose?
00:53:12 Yeah. Right? Well, yes, it did. It was trying to move a bunch of hot air from the equator to the
00:53:17 poles or something. That’s its purpose. But why? Because I seem to be equally as dumb today as I
00:53:23 was yesterday. So there’s some persistence, like a consistency over time that the intelligence
00:53:30 I plugged into. So like, what’s, it seems like there’s a hard constraint between the amount of
00:53:37 computation I can perform in my consciousness. Like they seem to be really closely connected
00:53:42 somehow. Well, I think the point is that the thing that gives you kind of the ability to have
00:53:48 kind of conscious intelligence, you can have kind of this, okay, so one thing is we don’t know
00:53:57 intelligences other than the ones that are very much like us. Yes. Right. And the ones that are
00:54:02 very much like us, I think have this feature of single thread of time, bounded, you know,
00:54:07 computationally bounded. But you also need computational sophistication. Having a single
00:54:14 thread of time and being computationally bounded, you could just be a clock going tick tock. That
00:54:19 would satisfy those conditions. But the fact that we have this sort of irreducible computational
00:54:27 ability, that’s an important feature. That’s sort of the bedrock on which we can construct
00:54:34 the things we construct. Now, the fact that we have this experience of the world that has the
00:54:40 single thread of time and computational boundedness, the thing that I sort of realized is it’s that
00:54:47 that causes us to deduce from this irreducible mess of what’s going on in the physical world,
00:54:53 the laws of physics that we think exist. So in other words, if we say, why do we believe that
00:55:00 there is, you know, continuous space, let’s say, why do we believe that gravity works the way it
00:55:06 does? Well, in principle, we could be kind of parsing details of the universe that were, you
00:55:14 know, that OK, the analogy is, again, with the statistical mechanics and molecules in a box,
00:55:22 we could be sensitive to every little detail of the swirling around of those molecules. And we
00:55:27 could say what really matters is the, you know, the wiggle effect that is, you know, that is
00:55:33 something that we humans just never noticed because it’s some weird thing that happens when
00:55:37 there are 15 collisions of air molecules and this happens and that happens. We just see the pure
00:55:42 motion of a ball moving about. Right. Why do we see that? Right. And the point is that that what
00:55:49 seems to be the case is that the things that if we say, given this sort of hypergraph that’s
00:55:55 updating and all the details about all the sort of atoms of space and what they do, and we say,
00:56:00 how do we slice that to what we can be sensitive to? What seems to be the case is that as soon as
00:56:06 we assume, you know, computational boundedness, single thread of time, that leads us to general
00:56:12 relativity. In other words, we can’t avoid that. That’s the way that we will parse the universe.
00:56:17 Given those constraints, we parse the universe according to those particular in such a way that
00:56:24 we say the aggregate reducible sort of pocket of computational reducibility that we slice out of
00:56:33 this kind of whole computational irreducible ocean of behavior is just this one that corresponds to
00:56:38 general relativity. Yeah, but we don’t perceive general relativity. Well, we do if we do fancy
00:56:44 experiments. So you’re saying so perceive really does mean the full. We drop something. That’s a
00:56:49 great example of general relativity in action. No, but like what’s the difference in that and
00:56:54 Newtonian mechanics? I mean, oh, it doesn’t. This is when I say general relativity, that’s
00:57:00 the uber theory, so to speak. I mean, Newtonian gravity is just the approximation that we can make,
00:57:05 you know, on the earth and things like that. So this is, you know, the phenomenon of gravity
00:57:11 is one that is a consequence of, you know, we would perceive something very different from
00:57:17 gravity. So so the way to understand that is when we think about OK, so we make up reference frames
00:57:26 with which we parse what’s happening in space and time. So in other words, one of the one of
00:57:31 the things that we do is we say as time progresses everywhere in space is something happens at a
00:57:40 particular time and then we go to the next time and we say this is what space is like at the next
00:57:44 time is what space is like at the next time. That’s it’s the reason we are used to doing that
00:57:51 is because, you know, when we look around, we might see, you know, ten hundred meters away.
00:57:57 The time it takes light to travel that distance is really short compared to the time it takes our
00:58:02 brains to know what happened. So as far as our brains are concerned, we are parsing the universe
00:58:08 in this. There is a moment in time, it’s all of space. There’s a moment in time, it’s all of
00:58:12 space. If we were the size of planets or something, we would have a different perception because the
00:58:17 speed of light would be much more important to us. We wouldn’t have this perception that
00:58:22 things happen progressively in time everywhere in space. And so that’s an important kind of
00:58:28 constraint. And the reason that we kind of parse the universe in the way that causes us to say
00:58:33 gravity works the way it does is because we’re doing things like deciding that we can say the
00:58:39 universe exists, space has a definite structure. There is a moment in time, space has this definite
00:58:45 structure. We move to the next moment in time, space has another structure. That kind of setup
00:58:50 is what lets us kind of deduce kind of what parse the universe in such a way that we say gravity
00:58:58 works the way it does. So that kind of reference frame is that the illusion of that is that you’re
00:59:05 saying that’s somehow useful for consciousness. That’s what consciousness does. Because in a
00:59:11 sense, what consciousness is doing is it’s insisting that the universe is kind of sequentialized.
00:59:21 And it is not allowing the possibility that, oh, there are these multiple threads of time
00:59:25 and they’re all flowing differently. It’s like saying, no, everything is happening in this one
00:59:31 thread of experience that we have. And that illusion of that one thread of experience
00:59:36 cannot happen at the planetary scale. Are you saying typical human, are you saying we are at a
00:59:41 human level is special here for consciousness? Well, for our kind of consciousness, if we existed
00:59:49 at a scale close to the elementary length, for example, then our perception of the universe
00:59:53 will be absurdly different. Okay. But this makes consciousness seem like a weird side effect to
00:59:58 this particular scale. And so who cares? I mean, consciousness is not that special.
01:00:05 Look, I think that a very interesting question is, which I’ve certainly thought a little bit about,
01:00:10 is what can you imagine? What is a sort of factoring of something? What are some other
01:00:16 possible ways you could exist, so to speak? And if you were a photon, if you were some kind of thing
01:00:23 that was kind of, you know, intelligence represented in terms of photons, you know,
01:00:30 for example, the photons we receive in the cosmic microwave background, those photons,
01:00:35 as far as they’re concerned, the universe just started. They were emitted, you know,
01:00:39 100,000 years after the beginning of the universe, they’ve been traveling at the speed of light,
01:00:43 time stayed still for them, and then they just arrived and we just detected them. So for them,
01:00:49 the universe just started. And that’s a different perception of, you know, that has
01:00:53 implications for a very different perception of time. They don’t have that single thread
01:00:57 that seems to be really important for being able to tell a heck of a good story.
01:01:01 So we humans, we can tell a story. Right. We can tell a story. What other kind of stories can you
01:01:07 tell? So photon is a really boring story. Yeah. I mean, so that’s a, I don’t know if they’re a
01:01:13 boring story, but I think it’s, you know, I’ve been wondering about this and I’ve been asking,
01:01:17 you know, friends of mine who are science fiction writers and things, have you written stuff about
01:01:20 this? And I’ve got one example, a great collection of books from my friend Rudy Rooker, which I have
01:01:28 to say, they’re books that are very informed by a bunch of science that I’ve done. And the thing
01:01:34 that I really loved about them is, you know, in the first chapter of the book, the Earth is consumed
01:01:41 by these things called nants, which are nano, nanobot type things. So, you know, so the Earth
01:01:47 is gone in the first, but then it comes back. But then, yeah, right. That was only a micro
01:01:53 spoiler. It’s only chapter one. But the thing that is not a real spoiler alert because it’s
01:02:01 such a complicated concept, but in the end, the Earth is saved by this thing called the
01:02:07 principle of computational equivalence, which is a kind of a core scientific idea of mine.
01:02:12 And I was just like, like thrilled. I don’t read fiction books very often. And I was just thrilled.
01:02:17 I get to the end of this and it’s like, oh, my gosh, you know, everything is saved by this sort
01:02:22 of deep scientific principle. Can you maybe elaborate how the principle of computational
01:02:27 equivalence can save a planet? That would, that would be a terrible spoiler. That would be a
01:02:36 spoiler. But no, but let me say what the principle of computational equivalence is. So the question
01:02:42 is, you are, you have a system, you have some rule, you can think of its behavior as corresponding
01:02:48 to a computation. The question is, how sophisticated is that computation? The statement of the principle
01:02:54 of computational equivalence is, as soon as it’s not obviously simple, it will be as sophisticated
01:03:00 as anything. And so that has the implication that, you know, rule 30, you know, our brains,
01:03:07 other things in physics, they’re all ultimately equivalent in the computations they can do.
01:03:12 And that’s what leads to this computational irreducibility idea because the reason we don’t
01:03:16 get to jump ahead, you know, and out think rule 30 is because we’re just computationally equivalent
01:03:22 to rule 30. So we’re kind of just both just running computations that are the same sort of
01:03:28 raw, the same level of computation, so to speak. So that’s kind of the idea there. And the question,
01:03:34 I mean, it’s like the, you know, in the science fiction version would be, okay, somebody says,
01:03:41 we just need more servers, get us more servers. The way to get even more servers is turn the
01:03:46 whole planet into a bunch of microservers. And that’s where it starts. And so the question of,
01:03:53 you know, computational equivalence, principle of computational equivalence is, well, actually,
01:03:57 you don’t need to build those custom servers. Actually, you can just use natural computation
01:04:06 to compute things, so to speak. You can use nature to compute. You don’t need to have done
01:04:11 all that engineering. I mean, it kind of feels a little disappointing that you say, we’re going to
01:04:16 build all these servers. We’re going to do all these things. We’re going to make, you know,
01:04:19 maybe we’re going to have human consciousness uploaded into, you know, some elaborate digital
01:04:25 environment. And then you look at that thing and you say, it’s got electrons moving around,
01:04:29 just like in a rock. And then you say, well, what’s the difference? And the principle of
01:04:33 computational equivalence says there isn’t, at some level, a fundamental, you know, you can’t say,
01:04:39 mathematically, there’s a fundamental difference between the rock that is the future of human
01:04:45 consciousness and the rock that’s just a rock. Now, what I’ve sort of realized with this kind
01:04:51 of consciousness thing is there is an aspect of this that seems to be more special. And for
01:04:59 example, something I haven’t really teased apart properly is when it comes to something like the
01:05:03 weather and the weather having a mind of its own or whatever, or your average, you know,
01:05:07 pulsar magnetosphere acting like a sort of intelligent thing, how does that relate to,
01:05:13 you know, how is that entity related to the kind of consciousness that we have? And sort of,
01:05:21 what would the world look like, you know, to the weather? If we think about the weather as a mind,
01:05:26 what will it perceive? What will its laws of physics be? I don’t really know.
01:05:31 Because it’s very parallel.
01:05:33 It’s very parallel, among other things. And it’s not obvious. I mean, this is a really kind of
01:05:39 mindbending thing because we’ve got to try and imagine a parsing of the universe different from
01:05:46 the one we have. And by the way, when we think about extraterrestrial intelligence and so on,
01:05:51 I think that’s kind of the key thing is, you know, we’ve always assumed, I’ve always assumed,
01:05:57 okay, the extraterrestrials, at least they have the same physics. We all live in the same universe.
01:06:01 They’ve got the same physics. But actually, that’s not really right because the extraterrestrials
01:06:07 could have a completely different way of parsing the universe. So it’s as if, you know, there could
01:06:12 be for all we know, right here in this room, you know, in the details of the motion of these gas
01:06:17 molecules, there could be an amazing intelligence that we were like, but we have no way of, we’re
01:06:24 not parsing the universe in the same way. If only we could parse the universe in the right way,
01:06:29 you know, immediately this amazing thing that’s going on and this, you know, huge culture that’s
01:06:34 developed and all that kind of thing would be obvious to us, but it’s not because we have our
01:06:38 particular way of parsing the universe. Would that thing also have an agency? I don’t know the right
01:06:43 word to use, but something like consciousness, but a different kind of consciousness?
01:06:47 I think it’s a question of just what you mean by the word, because I think that the,
01:06:51 you know, this notion of consciousness and the, okay, so some people think of consciousness as
01:06:56 sort of a key aspect of it is that we feel that there’s sort of a feeling of that we exist in
01:07:03 some way, that we have this intrinsic feeling about ourselves. You know, I suspect that any
01:07:11 of these things would also have an intrinsic feeling about themselves. I’ve been sort of
01:07:14 trying to think recently about constructing an experiment about what if you were just a piece
01:07:19 of a cellular automaton, let’s say, you know, what would your feeling about yourself actually be?
01:07:25 And, you know, can we put ourselves in the shoes, in the cells of the cellular automaton,
01:07:30 so to speak? Can we get ourselves close enough to that, that we could have a sense of what the
01:07:36 world would be like if you were operating in that way? And it’s a little difficult because,
01:07:42 you know, you have to not only think about what are you perceiving, but also what’s actually
01:07:46 going on in your brain. And our brains do what they actually do. And they don’t, it’s, you know,
01:07:52 I think there might be some experiments that are possible with neural nets and so on,
01:07:57 where you can have something where you can at least see in detail what’s happening inside the
01:08:02 system. And one of my projects to think about is, is there a way of kind of getting a sense
01:08:10 kind of from inside the system about what its view of the world is and how it, you know,
01:08:16 can we make a bridge? See, the main issue is this. It’s a sort of philosophically difficult thing
01:08:23 because it’s like we do what we do. We understand ourselves, at least to some extent.
01:08:29 We humans understand ourselves.
01:08:30 That’s correct. But yet, okay, so what are we trying to do, for example, when we are trying to
01:08:35 make a model of physics? What are we actually trying to do? Because, you know, you say, well,
01:08:40 can we work out what the universe does? Well, of course we can. We just watch the universe. The
01:08:44 universe does what it does. But what we’re trying to do when we make a model of physics is we’re
01:08:49 trying to get to the point where we can tell a story to ourselves that we understand that is also
01:08:54 a representation of what the universe does. So it’s this kind of, you know, can we make a bridge
01:08:59 between what we humans can understand in our minds and what the universe does? And in a sense,
01:09:05 you know, a large part of my kind of life efforts have been devoted to making computational
01:09:11 language, which kind of is a bridge between what is possible in the computational universe
01:09:16 and what we humans can conceptualize and think about. In a sense, when I built Wolfram Language
01:09:22 and our whole sort of computational language story, it’s all about how do you take sort of raw
01:09:28 computation and this ocean of computational possibility and how do we sort of represent
01:09:33 pieces of it in a way that we humans can understand and that map onto things that we care about doing.
01:09:39 And in a sense, when you add physics, you’re adding this other piece where we can, you know,
01:09:44 mediated by computer, can we get physics to the point where we humans can understand something
01:09:50 about what’s happening in it? And when we talk about an alien intelligence, it’s kind of the
01:09:55 same story. It’s like, is there a way of mapping what’s happening there onto something that we
01:10:00 humans can understand? And, you know, physics in some sense is like our exhibit one of the story
01:10:08 of alien intelligence. It’s an alien intelligence in some sense. And what we’re doing in making a
01:10:15 model of physics is mapping that onto something that we understand. And I think, you know, a lot
01:10:21 of these other things that I’ve recently been kind of studying, whether it’s molecular biology,
01:10:26 other kinds of things, which we can talk about a bit, those are other cases where we’re in a sense
01:10:33 trying to, again, make that bridge between what we humans understand and sort of the natural
01:10:39 language of that sort of alien intelligence in some sense. When you’re talking about,
01:10:44 just to backtrack a little bit about cellular automata, being able to, what’s it like to be
01:10:51 a cellular automata in the way that’s equivalent to what is it like to be a conscious human being?
01:10:58 How do you approach that? So is it looking at some subset of the cellular automata, asking questions
01:11:04 of that subset, like how the world is perceived, how you as that subset, like for that local pocket
01:11:13 of computation, what are you able to say about the broader cellular time? And that somehow then
01:11:21 can give you a sense of how to step outside of that cellular time. Right, but the tricky part is
01:11:25 that that little subset, what it’s doing is it has a view of itself. And the question is,
01:11:33 how do you get inside it? It’s like when we, with humans, it’s like we can’t get inside each other’s
01:11:40 consciousness. That doesn’t really even make sense. It’s like there is an experience that
01:11:47 somebody is having, but you can perceive things from the outside, but sort of getting inside
01:11:52 it, it doesn’t quite make sense. And for me, these sort of philosophical issues, and this one I have
01:11:58 not untangled, so let’s be… For me, the thing that has been really interesting in thinking
01:12:04 through some of these things is when it comes to questions about consciousness or whatever else,
01:12:09 it’s like when I can run a program and actually see pictures and make things concrete, I have a
01:12:16 much better chance to understand what’s going on than when I’m just trying to figure out what’s
01:12:20 going on. I have a much better chance to understand what’s going on than when I’m just trying to
01:12:24 reason about things in a very abstract way. Yeah, but there may be a way to map the program to your
01:12:32 conscious experience. So for example, when you play a video game, you do a first person shooter,
01:12:37 you walk around inside this entity. It’s a very different thing than watching this entity. So
01:12:43 connect more and more, connect this full conscious experience to the subset of the cellular automata.
01:12:51 Yeah, it’s something like that. But the difference in the first person shooter thing is there’s still
01:12:55 your brain and your memory is still remembering. You still have… It’s hard to… I mean, again,
01:13:02 what one’s going to get, one is not going to actually be able to be the cellular automaton.
01:13:08 One’s going to be able to watch what the cellular automaton does. But this is the frustrating thing
01:13:12 that I’m trying to understand how to think about being it, so to speak.
01:13:18 Okay. So like in virtual reality, there’s a concept of immersion, like with anything,
01:13:21 with video games, with books, there’s a concept of immersion. It feels like over time, if the
01:13:26 virtual reality experience is well done, and maybe in the future it’ll be extremely well done,
01:13:33 the immersion leads you to feel like… You mentioned memories. You forget that you even
01:13:40 ever existed outside that experience. It’s so immersive. I mean, you could argue sort of
01:13:46 mathematically that you can never truly become immersed, but maybe you can. I mean, why can’t you
01:13:52 merge with the cellular automata? I mean, aren’t you just part of the same fabric? Why can’t you
01:13:58 just like… Well, that’s a good question. I mean, so let’s imagine the following scenario. Let’s
01:14:02 imagine… Can you return? But then can you return back? Well, yeah, right. I mean, it’s like,
01:14:08 let’s imagine you’ve uploaded, your brain is scanned, you’ve got every synapse mapped out,
01:14:14 you upload everything about you, the brain simulator, you upload the brain simulator,
01:14:18 and the brain simulator is basically some glorified cellular automaton. And then you say,
01:14:25 well, now we’ve got an answer to what does it feel like to be a cellular automaton?
01:14:28 It feels just like it felt to be ordinary you, because they’re both computational systems,
01:14:34 and they’re both operating in the same way. But I think there’s somehow more to it,
01:14:39 because in that sense, when you’re just making a brain simulator, we’re just saying there’s
01:14:46 another version of our consciousness. The question that we’re asking is, if we tease away from our
01:14:50 consciousness and get to something that is different, how do we make a bridge to understanding
01:14:55 what’s going on there? And there’s a way of thinking about this. Okay, so this is coming
01:15:00 on to questions about the existence of the universe and so on. But one of the things is
01:15:05 there’s this notion that we have of ruleal space. So we have this idea of this physical space,
01:15:11 which is something you can move around in that’s associated with the extent of the
01:15:17 spatial hypergraph. Then there’s what we call branchial space, the space of quantum branches.
01:15:22 So in this thing we call the multiway graph of all of this branching histories,
01:15:28 there’s this idea of a kind of space where instead of moving around in physical space,
01:15:32 you’re moving from history to history, so to speak, from one possible history to another
01:15:36 possible history. And that’s kind of a different kind of space that is the space in which quantum
01:15:42 mechanics plays out. Quantum mechanics, for example, I think we’re slowly understanding
01:15:48 things like destructive interference in quantum mechanics, that what’s happening is branchial
01:15:53 space is associated with phase in quantum mechanics. And what’s happening is the two
01:15:58 photons that are supposed to be interfering and destructively interfering are winding up at
01:16:02 different ends of branchial space. And so us as these poor observers that have branching brains
01:16:09 that are trying to conflate together these different threads of history and say,
01:16:13 we’ve really got a consistent story that we’re telling here. We’re really knitting together
01:16:17 these threads of history. By the time the two photons wound up at opposite ends of branchial
01:16:22 space, we just can’t knit them together to tell a consistent story. So for us,
01:16:26 that’s sort of the analog of destructive interference. Got it. And then there’s
01:16:30 rule space too, which is the space of rules. Yes. Well, that’s another level up. So there’s
01:16:37 the question. Actually, I do want to mention one thing because it’s something I’ve realized in
01:16:42 recent times and I think it’s really, really kind of cool, which is about time dilation and
01:16:46 relativity. And it kind of helps to understand it’s something that kind of helps in understanding
01:16:51 what’s going on. So according to relativity, if you have a clock, it’s ticking at a certain rate,
01:16:58 you send it in a spacecraft that’s going at some significant fraction of the speed of light,
01:17:03 to you as an observer at rest, that clock that’s in the spacecraft will seem to be ticking much
01:17:09 more slowly. And so in other words, it’s kind of like the twin who goes off to Alpha Centauri and
01:17:16 goes very fast will age much less than the twin who’s on Earth that is just hanging out where
01:17:22 they’re hanging out. Okay, why does that happen? Okay, so it has to do with what motion is.
01:17:28 So in our models of physics, what is motion? Well, when you move from somewhere to somewhere,
01:17:35 you’re having to sort of recreate yourself at a different place in space.
01:17:40 When you exist at a particular place and you just evolve with time, again, you’re updating yourself,
01:17:46 you’re following these rules to update what happens. Well, so the question is, when you
01:17:51 have a certain amount of computation in you, so to speak, when there’s a certain amount,
01:17:55 you know, you’re computing, the universe is computing at a certain rate, you can either
01:17:59 use that computation to work out sitting still where you are, what’s going to happen successively
01:18:05 in time, or you can use that computation to recreate yourself as you move around the universe.
01:18:10 Mm hmm. And so time dilation ends up being, it’s really cool, actually, that this is explainable
01:18:16 in a way that isn’t just imagine the mathematics of relativity. But time dilation is a story of
01:18:21 the fact that as you kind of are recreating yourself as you move, you are using up some
01:18:27 of your computation. And so you don’t have as much computation left over to actually work out what
01:18:33 happens progressively with time. So that means that time is running more slowly for you because
01:18:38 it is, you’re using up your computation, your clock can’t tick as quickly, because every tick
01:18:45 of the clock is using up some computation, but you already use that computation up on moving at,
01:18:50 you know, half the speed of light or something. And so that’s why time dilation happens.
01:18:55 And so you can start, so it’s kind of interesting that one can sort of get an intuition about
01:19:00 something like that, because it has seemed like just a mathematical fact about the mathematics of
01:19:05 special relativity and so on. Well, for me, it’s a little bit confusing what the you in that picture
01:19:10 is, because you’re using up computation. Okay, so we’re simply saying the entity is updating
01:19:19 itself according to the way that the universe updates itself. And the question is, you know,
01:19:26 those updates, let’s imagine the you as a clock. Okay. And the clock is, you know, there’s all
01:19:31 these little updates, the hypergraph and a sequence of updates cause the pendulum to swing back the
01:19:37 other way, and then swing back, swinging back and forth. Okay. And all of those updates are
01:19:44 contributing to the motion of, you know, the pendulum going back and forth or the little
01:19:48 oscillator moving, whatever it is. Okay. But then the alternative is that sort of situation one,
01:19:54 where the thing is at rest, situation two, where it’s kind of moving, what’s happening is it is
01:20:00 having to recreate itself at every moment, the thing is going to have to do the computations
01:20:07 to be able to sort of recreate itself at a different position in space. And that’s kind of
01:20:12 the intuition behind, so it’s either going to spend its computation recreating itself at a
01:20:17 different position in space, or it’s going to spend its computation doing the sort of doing the
01:20:24 updating of the, you know, of the ticking of the clock, so to speak. So the more updating is doing,
01:20:30 the less the ticking of the clock update is doing. That’s right. The more it’s having to update
01:20:35 because of motion, the less it can update the clock. Obviously, there’s a sort of mathematical
01:20:42 version of it that relates to how it actually works in relativity, but that’s kind of, to me,
01:20:47 that was sort of exciting to me that it’s possible to have a really mechanically explainable story
01:20:52 there. And similarly in quantum mechanics, this notion of branching brains perceiving branching
01:20:58 universes, to me, that’s getting towards a sort of mechanically explainable version of what happens
01:21:03 in quantum mechanics, even though it’s a little bit mind bending to see, you know, these things
01:21:07 about under what circumstances can you successfully knit together those different threads of history,
01:21:13 and when do things sort of escape, and those kinds of things. But the thing about this physical space
01:21:21 and physical space, the main sort of big theory is general relativity, the theory of gravity,
01:21:26 and that tells you how things move in physical space. In branchial space, the big theory is the
01:21:32 Feynman path integral, which it turns out tells you essentially how things move in quantum in the
01:21:38 space of quantum phases. So it’s kind of like motion in branchial space. And it’s kind of a
01:21:43 fun thing to start thinking about all these things that we know in physical space, like event horizons
01:21:51 and black holes and so on. What are the analogous things in branchial space? For example, the speed
01:21:55 of light, what’s the analog of the speed of light in branchial space? It’s the maximum speed of
01:21:59 quantum entanglement. So the speed of light is a flash bulb goes off here. What’s the maximum rate
01:22:06 at which the effect of that flash bulb is detectable moving away in space? So similarly,
01:22:13 in branchial space, something happens. And the question is, how far in this branchial space,
01:22:18 in the space of quantum states, how far away can that get within a certain period of time?
01:22:23 And so there’s this notion of a maximum entanglement speed. And that might be observable.
01:22:28 That’s the thing we’ve been sort of poking at, is might there be a way to observe it,
01:22:32 even in some atomic physics kind of situation? Because one of the things that’s weird in
01:22:37 quantum mechanics is when we study quantum mechanics, we mostly study it in terms of small
01:22:44 numbers of particles. This electron does this, this thing on an ion trap does that and so on.
01:22:49 But when we deal with large numbers of particles, kind of all bets are off. It’s kind of too
01:22:52 complicated to deal with quantum mechanics. And so what ends up happening is, so this question
01:22:58 about maximum entanglement speed and things like that may actually play in the sort of story of
01:23:04 many body quantum mechanics and even have some suspicions about things that might happen even in
01:23:10 one of the things I realized I’d never understood and it’s kind of embarrassing, but I think I now
01:23:15 understand a little better, is when you have chemistry and you have quantum mechanics,
01:23:20 it’s like, well, there’s two carbon atoms in this molecule and we do a reaction and we draw a
01:23:25 diagram and we say this carbon atom ends up in this place. And it’s like, but wait a minute,
01:23:29 in quantum mechanics, nothing ends up in a definite place. There’s always just some wave
01:23:32 function for this to happen. How can it be the case that we can draw these reasonable, it just
01:23:37 ended up in this place? And you have to kind of say, well, the environment of the molecule
01:23:42 effectively made a bunch of measurements on the molecule to keep it kind of classical.
01:23:46 And that’s a story that has to do with this whole thing about measurements have to do with this
01:23:52 idea of, can we conclude that something definite happened? Because in quantum mechanics,
01:23:58 the intrinsic quantum mechanics, the mathematics of quantum mechanics is all about,
01:24:02 they’re just these amplitudes for different things to happen. Then there’s this thing of,
01:24:06 and then we make a measurement and we conclude that something definite happened. And that has
01:24:11 to do with this thing, I think, about sort of moving about knitting together these different
01:24:16 threads of history and saying, this is now something where we can definitively say something
01:24:20 definite happened. In the traditional theory of quantum mechanics, it’s just like, after you’ve
01:24:25 done all this amplitude computation, then this big hammer comes down and you do a measurement
01:24:30 and it’s all over. And that’s been very confusing. For example, in quantum computing,
01:24:34 it’s been a very confusing thing because when you say, in quantum computing, the basic idea is
01:24:39 you’re going to use all these separate threads of computation, so to speak, to do all the different
01:24:44 parts of, try these different factors for an integer or something like this. And it looks
01:24:48 like you can do a lot because you’ve got all these different threads going on. But then you have to
01:24:53 say, well, at the end of it, you’ve got all these threads and every thread came up with a definite
01:24:57 answer, but we got to conflate those together to figure out a definite thing that we humans
01:25:02 can take away from it, a definite, so the computer actually produced this output.
01:25:06 So having this branchial space and this hypergraph model of physics, do you think it’s possible to
01:25:14 then make predictions that are definite about many body quantum mechanical systems?
01:25:21 I think it’s likely, yes. Every one of these things, when you go from the underlying theory,
01:25:28 which is complicated enough and it’s, I mean, the theory at some level is beautifully simple,
01:25:33 but as soon as you start actually trying to, it’s this whole question about how do you bridge it to
01:25:37 things that we humans can talk about, it gets really complicated. And this thing about actually
01:25:43 getting it to a definite prediction about definite thing you can say about chemistry or something
01:25:50 like this, that’s just a lot of work. So I’ll give you an example. There’s a thing called the
01:25:54 quantum Zeno effect. So the idea is quantum stuff happens, but then if you make a measurement,
01:26:01 you’re kind of freezing time in quantum mechanics. So it looks like there’s a possibility that with
01:26:08 sort of the relationship between the quantum Zeno effect and the way that many body quantum
01:26:12 mechanics works and so on, maybe just conceivably, it may be possible to actually figure out a way
01:26:18 to measure the maximum entanglement speed. And the reason we can potentially do that
01:26:23 is because the systems we deal with in terms of atoms and things, they’re pretty big. A mole of
01:26:29 atoms is a lot of atoms, but it’s something where to get, when we’re dealing with how can you see
01:26:37 10 to the minus 100, so to speak? Well, by the time you’ve got 10 to the 30th atoms, you’re within
01:26:45 a little bit closer striking distance of that. It’s not like, oh, we’ve just got two atoms and
01:26:51 we’re trying to see down to 10 to the minus 100 meters or whatever. So I don’t know how it will
01:26:56 work, but this is a potential direction. And if you can tell, by the way, if we could measure
01:27:02 the maximum entanglement speed, we would know the elementary length. These are all related.
01:27:07 So if we get that one number, we just need one number. If we can get that one number,
01:27:13 the theory has no parameters anymore. And there are other places, well, there’s another hope for
01:27:20 doing that is in cosmology. In this model, one of the features is the universe is not fixed
01:27:25 dimensional. We think we live in three dimensional space, but this hypergraph doesn’t have any
01:27:29 particular dimension. It can emerge as something which on an approximation, it’s as if you say,
01:27:36 what’s the volume of a sphere in the hypergraph where a sphere is defined as how many nodes do
01:27:41 you get to when you go a distance R away from a given point? And you can say, well, if I get to
01:27:47 about R cubed nodes, when I go a distance R away in the hypergraph, then I’m living roughly in
01:27:52 three dimensional space. But you might also get to R to the point 2.92 for some value of R. As R
01:28:02 increases, that might be the sort of fit to what happens. And so one of the things we suspect is
01:28:07 that the very early universe was essentially infinite dimensional, and that as the universe
01:28:13 expanded, it became lower dimensional. And so one of the things that is another little sort of point
01:28:19 where we think there might be a way to actually measure some things is dimension fluctuations in
01:28:24 the early universe. That is, is there leftover dimension fluctuation of at the time of the cosmic
01:28:30 microwave background, 100,000 years or something after the beginning of the universe? Is it still
01:28:34 the case that there were pieces of the universe that didn’t have dimension three, that had
01:28:39 dimension 3.01 or something? And can we tell that? Is that possible to observe fluctuations in
01:28:47 dimensions? I don’t even know what that entails. Okay. So the question, which should be an
01:28:54 elementary exercise in electrodynamics, except it isn’t, is understanding what happens to a
01:28:59 photon when it propagates through 3.01 dimensional space. So for example, the inverse square law
01:29:05 is a consequence of the surface area of a sphere is proportional to R squared. But if you’re not
01:29:13 in three dimensional space, the surface area of sphere is not proportional to R squared. It’s R
01:29:19 to the whatever 2.01 or something. And so that means that I think when you kind of try and do
01:29:27 optics, you know, a common principle in optics is Huygens principle, which basically says that every
01:29:32 piece of a wave front of light is a source of new spherical waves. And those spherical waves,
01:29:40 if they’re different dimensional spherical waves, will have other characteristics. And so there will
01:29:46 be bizarre optical phenomena which we haven’t figured out yet. So you’re looking for some weird
01:29:53 photon trajectories that designate that it’s 3.01 dimensional space? Yeah. Yeah. That would be an
01:30:01 example of, I mean, you know, there are only a certain number of things we can measure about
01:30:05 photons. You know, we can measure their polarization, we can measure their frequency,
01:30:09 we can measure their direction, those kinds of things. And, you know, how that all works out.
01:30:15 And, you know, in the current models of physics, you know, it’s been hard to explain how the
01:30:21 universe manages to be as uniform as it is. And that’s led to this inflation idea that,
01:30:26 to the great annoyance of my then collaborator, we figured out in like 1979, we had this
01:30:32 realization that you could get something like this. But it seemed implausible that that’s the
01:30:36 way the universe worked. So we put it in a footnote. But in any case, I’ve never really
01:30:43 completely believed it. But that’s an idea for how to sort of puff out the universe faster than the
01:30:48 speed of light, early moments of the universe. That’s the sort of the inflation idea and that
01:30:54 you can somehow explain how the universe manages to be as uniform as it is. In our model, this turns
01:31:01 out to be much more natural because the universe just starts very connected. The hypergraph is not
01:31:07 such that the ball that you grow starting from a single point has volume R cubed, it might have
01:31:12 volume R to the 500 or R to the infinity. And so that means that you sort of naturally get this
01:31:19 much higher degree of connectivity and uniformity in the universe. And then the question is,
01:31:24 this is sort of the mathematical physics challenge, is in the standard theory of the universe,
01:31:29 there’s the Friedman Robertson Walker universe, which is the kind of standard model where the
01:31:33 universe is isotropic and homogeneous. And you can then work out the equations of general relativity,
01:31:38 and you can figure out how the universe expands. We would like to do the same kind of thing,
01:31:42 including dimension change. This is just difficult mathematical physics. I mean,
01:31:47 the reason it’s difficult is the sort of fundamental reason it’s difficult. When
01:31:51 people invented calculus 300 years ago, calculus was a story of understanding change and change
01:31:58 as a function of a variable. So people study univariate calculus, they study multivariate
01:32:03 calculus, it’s one variable, it’s two variables, three variables. But whoever studied, you know,
01:32:08 2.5 variable calculus, turns out nobody. Turns out that what we need to have to understand these
01:32:16 fractional dimensional spaces, which don’t work like well, they’re spaces where the effective
01:32:23 dimension is not an integer. So you can’t apply the tools of calculus naturally and easily to
01:32:30 fractional dimensions? No. So somebody has to figure out how to do that. Yeah,
01:32:34 we’re trying to figure this out. I mean, it’s very interesting. I mean, it’s very connected to
01:32:39 very frontier issues in mathematics. It’s very beautiful. So is it possible? Is it possible?
01:32:44 We’re dealing with a scale that’s so, so much smaller than our human scale. Is it possible
01:32:51 to make predictions versus explanations? Do you have a hope that with this hypergraph model,
01:32:57 you’d be able to make predictions that then could be validated with a physics experiment,
01:33:04 predictions that couldn’t have been done or weren’t done otherwise? Yeah, yeah, yeah. I mean,
01:33:08 you know, I think which, in which domain do you think? Okay, so they’re going to be cosmology ones
01:33:12 to do with dimension fluctuations in the universe. That’s a very bizarre effect. Nobody, you know,
01:33:16 dimension fluctuations is just something nobody ever looked for that. If anybody sees dimension
01:33:20 fluctuation, that’s a huge flag that something like our model is going on. And how one detects
01:33:27 that, you know, that’s a problem of kind of, you know, that’s a problem of traditional physics in
01:33:32 a sense of what’s the best way to actually figure that out. And for example, that’s one,
01:33:37 there are all kinds of things one could imagine. I mean, there are things that in black hole mergers,
01:33:44 it’s possible that there will be effects of maximum entanglement speed in large black hole mergers.
01:33:50 That’s another possible thing. And all of that is detected through like what? Do you have a
01:33:55 hope for LIGO type of situation? Like that’s gravitational waves? Yeah. Or alternatively,
01:34:01 I mean, I think it’s, you know, look, figuring out experiments is like figuring out technology
01:34:07 inventions. That is, you know, you’ve got a set of raw materials, you’ve got an underlying model,
01:34:12 and now you’ve got to be very clever to figure out, you know, what is that thing I can measure
01:34:16 that just somehow, you know, leverages into the right place. And we’ve spent less effort on that
01:34:23 than I would have liked. Because one of the reasons is that I think that the physicists
01:34:30 who’ve been working on our models, with now lots of physicists actually, it’s very, very nice. It’s
01:34:35 kind of, it’s one of these cases where I’m almost, I’m really kind of pleasantly surprised that the
01:34:41 sort of absorption of the things we’ve done has been quite rapid and quite sort of, you know,
01:34:47 very positive. So it’s a Cambrian explosion of physicists too, not just ideas. Yes. I mean,
01:34:53 you know, a lot of what’s happened that’s really interesting, and again, not what I expected,
01:34:57 is there are a lot of areas of sort of very elaborate, sophisticated mathematical physics,
01:35:04 whether that’s causal set theory, whether it’s higher category theory, whether it’s categorical
01:35:08 quantum mechanics, all sorts of elaborate names for these things, spin networks, perhaps,
01:35:14 you know, causal dynamical triangulations, all kinds of names of these fields. And these fields
01:35:20 have a bunch of good mathematical physicists in them who’ve been working for decades in these
01:35:24 particular areas. And the question is, but they’ve been building these mathematical structures.
01:35:30 And the mathematical structures are interesting, but they don’t typically sit on anything.
01:35:34 They’re just mathematical structures. And I think what’s happened is our models provide kind of
01:35:39 a machine code that lives underneath those models. So a typical example, this is due to
01:35:46 Jonathan Gorod, who’s one of the key people who’s been working on our project. This is in,
01:35:52 okay, so I’ll give you an example just to give a sense of how these things connect. This is in
01:35:56 causal set theory. So the idea of causal set theory is there are, in spacetime, we imagine
01:36:03 that there’s space and time. It’s a three plus one dimensional, you know, setup. We imagine that
01:36:09 there are just events that happen at different times and places in space and time. And the idea
01:36:16 of causal set theory is the only thing you say about the universe is there are a bunch of events
01:36:20 that happen sort of randomly at different places in space and time. And then the whole sort of
01:36:25 theory of physics has to be to do with this graph of causal relationships between these randomly
01:36:32 thrown down events. So they’ve always been confused by the fact that to get even Lorentz
01:36:37 invariants, even relativistic invariants, you need a very special way to throw down those events.
01:36:42 And they’ve had no natural way to understand how that would happen. So what Jonathan figured out
01:36:48 is that, in fact, from our models, instead of just generating events at random, our models
01:36:56 necessarily generate events in some pattern in spacetime effectively that then leads to Lorentz
01:37:02 invariants and relativistic invariants and all those kinds of things. So it’s a place where
01:37:06 all the mathematics that’s been done on, well, we just have a random collection of events.
01:37:10 Now what consequences does that have in terms of causal set theory and so on? That can all be kind
01:37:16 of wheeled in now that we have some different underlying foundational idea for what the
01:37:22 particular distribution of events is as opposed to just what we throw down random events.
01:37:26 And so that’s a typical sort of example of what we’re seeing in all these different areas of kind
01:37:32 of how you can take really interesting things that have been done in mathematical physics
01:37:36 and connect them. And it’s really kind of beautiful because the abstract models we have
01:37:43 just seem to plug into all these different very interesting, very elegant abstract ideas.
01:37:48 But we’re now giving sort of a reason for that to be the way, a reason for one to care. I mean,
01:37:54 it’s like saying you can think about computation abstractly. You can think about, I don’t know,
01:38:01 combinators or something as abstract computational things. And you can sort of do all kinds of study
01:38:06 of them. But it’s like, why do we care? Well, okay, Turing machines are a good start because
01:38:11 you can kind of see they’re sort of mechanically doing things. But when we actually start thinking
01:38:14 about computers, computing things, we have a really good reason to care. And this is sort of
01:38:19 what we’re providing, I think, is a reason to care about a lot of these areas of mathematical
01:38:24 physics. So that’s been very nice. So I’m not sure we’ve ever got to the
01:38:30 question of why does the universe exist at all? No, no, let’s talk about that. So it’s not the
01:38:36 simplest question in the world. So it takes a few steps to get to it. And it’s nevertheless even
01:38:42 surprising that you can even begin to answer this question, as you were saying.
01:38:46 Indeed. I’m very surprised. So the next thing to perhaps understand is this idea of ruleal space.
01:38:55 So we’ve got kind of physical space. We’ve got branchial space, the space of possible quantum
01:39:00 histories. And now we’ve got another level of kind of abstraction, which is ruleal space. And
01:39:05 here’s where that comes from. So you say, okay, you say we’ve got this model for the universe.
01:39:12 We’ve got a particular rule. And we run this rule and we get the universe. So that’s interesting.
01:39:19 Why that rule? Why not another rule? And so that confused me for a long time. And I realized,
01:39:25 well, actually, what if the thing could be using all possible rules? What if at every step,
01:39:31 in addition to saying apply a particular rule at all places in this hypergraph, one could say,
01:39:37 just take all possible rules and apply all possible rules at all possible places in this
01:39:41 hypergraph. And then you make this ruleal multiway graph, which both is all possible
01:39:48 histories for a particular rule and all possible rules. So the next thing you’d say is, how can you
01:39:53 get anything reasonable out of it? How can anything real come out of the set of all possible
01:39:58 rules applied in all possible ways? This is a subtle thing, which I haven’t fully untangled.
01:40:05 There is this object, which is the result of running all possible rules in all possible ways.
01:40:11 And you might say, if you’re running all possible rules, why can’t everything possible happen?
01:40:15 Well, the answer is because when you, there’s sort of this entanglement that occurs.
01:40:21 So let’s say that you have a lot of different possible initial conditions, a lot of different
01:40:27 possible states. Then you’re applying these different rules. Well, some of those rules can
01:40:32 end up with the same state. So it isn’t the case that you can just get from anywhere to anywhere.
01:40:37 There’s this whole entangled structure of what can lead to what, and there’s a definite structure
01:40:42 that’s produced. I think I’m going to call that definite structure the rulead, the limit of kind
01:40:48 of all possible rules being applied in all possible ways. And you’re saying that structure is finite,
01:40:54 so that somehow connects to maybe a similar kind of thing as like causal invariance.
01:40:59 Well, it happens that the rulead necessarily has causal invariance. That’s a feature of,
01:41:03 that’s just a mathematical consequence of essentially using all possible rules
01:41:08 plus universal computation gives you the fact that from any diverging paths, the paths will
01:41:14 always converge. But does that necessarily infer that the rulead is finite?
01:41:21 In the end, it’s not necessarily finite. I mean, just like the history of the universe may not be
01:41:28 finite. The history of the universe, time may keep going forever. You can keep running the
01:41:32 computations of the rulead and you’ll keep spewing out more and more and more structure. It’s like
01:41:37 time doesn’t have to end. But the issue is there are three limits that happen in this rulead
01:41:45 object. One is how long you run the computation for. Another is how many different rules you’re
01:41:51 applying. And another is how many different states you start from. And the mixture of those
01:41:56 three limits. I mean, this is just mathematically a horrendous object. And what’s interesting about
01:42:02 this object is the one thing that does seem to be the case about this object is it connects with
01:42:07 ideas in higher category theory. And in particular, it connects to some of the 20th century’s most
01:42:12 abstract mathematics done by this chap Grothendieck. Grothendieck had a thing called the infinity
01:42:18 groupoid, which is closely related to this rulead object. Although the details of the relationship,
01:42:24 you know, I don’t fully understand yet. But I think that what’s interesting is this thing that
01:42:31 is sort of this very limiting object. So, okay, so a way to think about this that, again, will
01:42:37 take us into another direction, which is the equivalence between physics and mathematics.
01:42:42 The way that, well, let’s see, maybe this is just to give a sense of this kind of groupoid and
01:42:50 things like that. You can think about, in mathematics, you can think you have certain axioms,
01:42:55 they’re kind of like atoms, and you, well, actually, let’s say, let’s talk about mathematics
01:43:01 for a second. So what is mathematics? What is it made of, so to speak? Mathematics, there’s a bunch
01:43:06 of statements, like, for addition, x plus y is equal to y plus x, that’s a statement in mathematics.
01:43:13 Another statement would be, you know, x squared minus one is equal to x plus one, x minus one.
01:43:18 There are an infinite number of these possible statements of mathematics.
01:43:21 Well, it’s not, I mean, it’s not just, I guess, a statement, but with x plus y,
01:43:25 it’s a rule that you can, I mean, you think of it as a rule.
01:43:29 It is a rule. It’s also just a thing that is true in mathematics.
01:43:35 Right. The statement of truth, okay.
01:43:37 Right. And what you can imagine is, you imagine just laying out this giant kind of ocean
01:43:44 of all statements. Well, actually, you first start, okay, this is where this was segueing
01:43:49 into a different thing. Let me not go in this direction for a second.
01:43:52 Let’s not go to metamathematics just yet.
01:43:54 Yeah, we’ll maybe get to metamathematics, but it’s, so let me not, let me explain the groupoid
01:44:00 and things later. But, so let’s come back to the universe, always a good place to be in,
01:44:07 so to speak.
01:44:07 Yeah, so what does the universe have to do with the rule add, the rule of L space,
01:44:11 and how that’s possibly connected to why the thing exists at all, and why there’s just
01:44:17 one of them?
01:44:18 Yes. Okay. So here’s the point. So the thing that had confused me for a long time was,
01:44:24 let’s say we get the rule for the universe. We hold it in our hand. We say, this is our
01:44:28 universe. Then the immediate question is, well, why isn’t it another one? And that’s
01:44:33 kind of the sort of the lesson of Copernicus is, we’re not very special. So how come we
01:44:39 got universe number 312 and not universe quadrillion, quadrillion, quadrillion? And
01:44:46 I think the resolution of that is the realization that the universe is running all possible
01:44:52 rules. So then you say, well, how on earth do we perceive the universe to be running
01:44:58 according to a particular rule? How do we perceive definite things happening in the
01:45:02 universe? Well, it’s the same story. It’s the observer, there is a reference frame that
01:45:08 we are picking in this ruleal space, and that that is what determines our perception of
01:45:14 the universe. With our particular sensory information and so on, we are parsing the
01:45:18 universe in this particular way. So here’s the way to think about it. In physical space,
01:45:24 we live in a particular place in the universe. And we could live on Alpha Centauri, but we
01:45:29 don’t. We live here. And similarly, in ruleal space, we could live in many different places
01:45:36 in ruleal space, but we happen to live here. And what does it mean to live here? It means
01:45:41 we have certain sensory input. We have certain ways to parse the universe. Those are our
01:45:47 interpretation of the universe. What would it mean to travel in ruleal space? What it
01:45:51 basically means is that we are successively interpreting the universe in different ways.
01:45:56 So in other words, to be at a different point in ruleal space is to have a different, in a sense,
01:46:01 a different interpretation of what’s going on in the universe. And we can imagine even
01:46:06 things like an analog of the speed of light as the maximum speed of translation in ruleal
01:46:10 space and so on. So wait, what’s the interpretation? So ruleal space and we,
01:46:18 I’m confused by the we and the interpretation and the universe. I thought moving about in
01:46:23 ruleal space changes the way the universe is. The way we would perceive it. So it ultimately
01:46:33 has to do with the perception. So it doesn’t real, ruleal space is not somehow changing,
01:46:41 like branching into another universe or something like that. No, I mean, the point is that the whole
01:46:47 point of this is the rule yard is sort of the encapsulated version of everything that is the
01:46:54 universe running according to all possible rules. We think of our universe, the observable universe,
01:47:00 as a thing. So we’re a little bit loose with the word universe then, because wouldn’t the rule yard
01:47:07 potentially encapsulate a very large number, like combinatorially large, maybe infinite
01:47:14 set of what we human physicists think of as universes? That’s an interesting, interesting
01:47:20 parsing of the word universe, right? Because what we’re saying is, just as we’re at a particular
01:47:25 place in physical space, we’re at a particular place in ruleal space, at that particular place
01:47:30 in ruleal space, our experience of the universe is this. Just as if we lived at the center of the
01:47:35 galaxy, our universe, our experience of the universe will be different from the one it is,
01:47:39 given where we actually live. And so what we’re saying is, you might say, I mean, in a sense,
01:47:47 this rule yard is sort of a super universe, so to speak. But it’s all entangled together. It’s not
01:47:52 like you can separate out. You can say, let me, it’s like when we take a reference, okay, it’s like
01:47:58 our experience of the universe is based on where we are in the universe. We could imagine moving
01:48:03 to somewhere else in the universe, but it’s still the same universe.
01:48:05 So there’s not like universes existing in parallel?
01:48:10 No. Because, and the whole point is that if we were able to change our interpretation of what’s
01:48:18 going on, we could perceive a different reference frame in this rule yard.
01:48:24 Yeah, but that’s not, that’s just, yeah, that’s the same rule yard. That’s the same universe.
01:48:31 You’re just moving about. These are just coordinates in the universe.
01:48:34 Right. So the reason that’s interesting is, imagine the extraterrestrial intelligence,
01:48:39 so the alien intelligence, we should say. The alien intelligence might live on Alpha Centauri,
01:48:46 but it might also live at a different place in real space.
01:48:48 It can live right here on Earth. It just has a different reference frame that
01:48:52 includes a very different perception of the universe. And then because that
01:48:57 real space is very large, I mean,
01:49:01 Do we get to communicate with them? Right.
01:49:04 Yeah, but it’s also, well, one thing is how different the perception of the universe could be.
01:49:13 I think it could be bizarrely, unimaginably completely different. And I mean, one thing to
01:49:19 realize is, even in kind of things I don’t understand well, you know, I know about the kind
01:49:25 of Western tradition of understanding, you know, science and all that kind of thing. And, you know,
01:49:30 you talk to people who say, well, I, you know, I’m really into some, you know, Eastern tradition of
01:49:36 this, that and the other. And it’s really obvious to me how things work. I don’t understand it
01:49:41 at all. But, you know, it is not obvious, I think, with this kind of realization that there’s these
01:49:47 very different ways to interpret what’s going on in the universe. That kind of gives me at least,
01:49:52 it doesn’t help me to understand that different interpretation. But it gives me at least more
01:49:57 respect for the possibility that there will be other interpretations.
01:49:59 Yeah, it humbles you to the possibility that like, what is it, reincarnation or all these like
01:50:06 eternal recurrence with Nietzsche, like just these ideas? Yeah.
01:50:12 Well, you know, the thing that I realized about a bunch of those things is that, you know,
01:50:15 I’ve been sort of doing my little survey of the history of philosophy, just trying to understand,
01:50:20 you know, what can I actually say now about some of these things? And you realize that some of
01:50:24 these concepts like the immortal soul concept, which, you know, I remember when I was a kid,
01:50:29 and, you know, it was kind of a lots of religion bashing type stuff of people saying, you know,
01:50:35 well, we know about physics, tell us how much does a soul weigh? And people are like, well,
01:50:41 how can it be a thing if it doesn’t weigh anything? Well, now we understand, you know,
01:50:46 there is this notion of what’s in brains that isn’t the matter of brains, and it’s something
01:50:50 computational. And there is a sense and in fact, it is correct, that it is in some sense, immortal,
01:50:56 because this pattern of computation is something abstract that is not specific to the particular
01:51:01 material of a brain. Now, we don’t know how to extract it, you know, in our traditional scientific
01:51:07 approach. But it’s still something where it isn’t a crazy thing to say there is something doesn’t
01:51:13 weigh anything. That’s a kind of a silly question. How much does it weigh? Well, actually, maybe it
01:51:19 isn’t such a silly question in our model of physics, because the actual computational activity
01:51:24 has has a consequence for gravity and things, but that’s a very subtle.
01:51:27 You can talk about mass and energy and so on. That could be a, what would you call it, a solitron.
01:51:35 Yes, yes, yes.
01:51:36 A particle that somehow contains soulness.
01:51:39 Yeah, right. Well, that’s what, by the way, that’s what Leibniz said. And, you know,
01:51:43 one thing I’ve never understood this, you know, Leibniz had this idea of monads and monadology,
01:51:48 and he had this idea that what exists in the universe is this big collection of monads.
01:51:53 And that they that the only thing that one knows about the monads is sort of how they relate to
01:51:57 each other. It sounds awfully like hypergraphs, right? But Leibniz had really lost me at the
01:52:02 following thing. He said, each of these monads has a soul, and each of them has a consciousness.
01:52:09 And it’s like, okay, I’m out of here. I don’t understand this at all. I don’t know what’s
01:52:12 going on. But I realized recently that in his day, the concept that a thing could do something
01:52:19 could spontaneously do something. That was his only way of describing that.
01:52:23 And so what I would now say is, well, there’s this abstract rule that runs. To Leibniz,
01:52:29 that would have been, you know, in 1690 or whatever, that would have been kind of,
01:52:33 well, it has a soul, it has a consciousness. And so, you know, in a sense, it’s like one
01:52:38 of these, there’s no new idea under the sun, so to speak. That’s a sort of a version of the same
01:52:43 kinds of ideas, but couched in terms that are sort of bizarrely different from the ones that
01:52:48 we would use today. Would you be able to maybe play devil’s advocate on your conception of
01:52:54 consciousness that, like the two characteristics of it that is constrained, and there’s a
01:52:59 single thread of time? Is it possible that Leibniz was onto something that the basic atom,
01:53:07 the discrete atom of space has a consciousness? Is that, so these are just words, right? But like,
01:53:14 what is there? Is there some sense where consciousness is much more fundamental
01:53:20 than you’re making it seem? I don’t know. I mean, you know, I think…
01:53:24 Can you construct a world in which it is much more fundamental?
01:53:27 I think that, okay, so the question would be, is there a way to think about kind of,
01:53:33 if we sort of parse the universe down at the level of atoms of space or something,
01:53:38 could we say, well, so that’s really a question of a different point of view,
01:53:42 a different place in real space. We’re asking the question, could there be a civilization
01:53:47 that exists? Could there be sort of conscious entities that exist at the level of atoms of
01:53:54 space? And what would that be like? And I think that comes back to this question of,
01:53:58 what’s it like to be a cellular automaton type thing? I mean, I’m not yet there. I don’t know.
01:54:05 I mean, I think that this is a… And I know I don’t even know yet quite how to think about this
01:54:12 in the sense that I was considering, you know, I never write fiction, but I haven’t written it
01:54:17 since I was like 10 years old. And my fiction, I made one attempt, which I sent to some science
01:54:22 fiction writer friends of mine, and they told me it was terrible. So, but…
01:54:25 This is a long time ago?
01:54:26 No, this is recently.
01:54:27 Recently. They said it was terrible. That’d be interesting to see you write a short story
01:54:31 based on what sounds like it’s already inspiring short stories or stories by science fiction
01:54:38 writers.
01:54:38 But I think the interesting thing for me is, you know, what is it like to be a whatever?
01:54:45 How do you describe that? I mean, that’s not a thing that you describe in mathematics,
01:54:49 the what is it like to be such and such.
01:54:51 Well, see, to me, when you say what is it like to be something,
01:54:55 it presumes that you’re talking about a singular entity. So, like, there’s some kind of feeling of
01:55:07 the entity, the stuff that’s inside of it and the stuff that’s outside of it.
01:55:12 And then that’s when consciousness starts making sense. But then it seems like that could be
01:55:20 generalizable. If you take some subset of a cellular automata, you could start talking
01:55:26 about what does that subset feel. But then you can, I think you could just take arbitrary
01:55:34 numbers of subsets. Like, to me, like, you and I individually are consciousnesses,
01:55:41 but you could also say the two of us together is a singular consciousness.
01:55:45 Maybe, maybe. I’m not so sure about that. I think that the single thread of time thing
01:55:49 may be pretty important. And that as soon as you start saying, there are two different threads
01:55:54 of time, there are two different experiences, and then we have to say, how do they relate?
01:55:59 How are they sort of entangled with each other? I mean, that may be a different story of a thing
01:56:03 that isn’t much like, you know, what do the ants, you know, what’s it like to be an ant,
01:56:08 you know, where there’s a sort of more collective view of the world, so to speak?
01:56:12 I don’t know. I think that, I mean, this is, you know, I don’t really have a good, I mean,
01:56:20 you know, my best thought is, you know, can we turn it into a human story? It’s like the question
01:56:26 of, you know, when we try and understand physics, can we turn that into something which is sort of
01:56:30 a human understandable narrative? And now what’s it like to be a such and such? You know, maybe the
01:56:36 only medium in which we can describe that is something like fiction, where it’s kind of like
01:56:41 you’re telling, you know, the life story in that setting. But I’m, this is beyond what I’ve yet
01:56:48 understood how to do. Yeah, but it does seem so, like with human consciousness, you know,
01:56:53 we’re made up of cells and like, there’s a bunch of systems that are networked that work together
01:57:01 that at this, at the human level, feel like a singular consciousness when you take, and so
01:57:07 maybe like an ant colony is just too low level. Sorry, an ant is too low level. Maybe you have to
01:57:14 look at the ant colony. Yeah, I agree. There’s some level at which it’s a conscious being. And then
01:57:20 if you go to the planetary scale, then maybe that’s going too far. So there’s a nice sweet spot for
01:57:26 consciousness. No, I agree. I think the difficulty is that, you know, okay, so in sort of people who
01:57:33 talk about consciousness, one of the terrible things I’ve realized, because I’ve now interacted
01:57:38 with some of this community, so to speak, some interesting people who do that kind of thinking.
01:57:44 But, you know, one of the things I was saying to one of the leading people in that area, I was
01:57:48 saying, you know, that, you know, it must be kind of frustrating because it’s kind of like a poetry
01:57:55 story. That is many people are writing poems, but few people are reading them. So there are always
01:57:59 these different, you know, everybody has their own theory of consciousness, and they are very
01:58:04 non inter sort of inter discussable. And by the way, I mean, you know, my own approach to sort of
01:58:11 the question of consciousness, as far as I’m concerned, I’m an applied consciousness operative,
01:58:16 so to speak, because I don’t really, in a sense, the thing I’m trying to get out of it is how does
01:58:21 it help me to understand what’s a possible theory of physics? And how does it help me to say,
01:58:27 how do I go from this incoherent collection of things happening in the universe to our definite
01:58:34 perception and definite laws and so on, and sort of an applied version of consciousness? And I
01:58:38 think the reason it sort of segues to a different kind of topic, but the reason that one of the
01:58:44 things I’m particularly interested in is kind of what’s the analog of consciousness in systems
01:58:48 very different from brains? And so why is that matter? Well, you know, this whole description
01:58:54 of this kind of, you know what, we haven’t talked about why the universe exists. So let’s get to why
01:59:00 the universe exists. And then we can talk about perhaps a little bit about what these models of
01:59:06 physics kind of show you about other kinds of things like molecular computing and so on.
01:59:12 Yes, that’s good.
01:59:13 Why does the universe exist? Okay, so we finally sort of more or less set the stage,
01:59:17 we’ve got this idea of this rule yard of this object that is made from following all possible
01:59:22 rules, the fact that it’s sort of not just this incoherent mess, it’s got all this entangled
01:59:27 structure in it, and so on. Okay, so what is this rule yard? Well, it is the working out of all
01:59:35 possible formal systems. So the sort of the question of why does the universe exist? Its
01:59:41 core question, which we kind of started with is, you’ve got two plus two equals four, you’ve got
01:59:46 some other abstract result, but that’s not actualized. It’s just an abstract thing.
01:59:52 And when we say we’ve got a model for the universe, okay, it’s this rule, you run it,
01:59:56 and it’ll make the universe, but it’s like, but where’s it actually running? What is it actually
02:00:03 doing? Is it actual, or is it merely a formal description of something? So the thing to realize
02:00:11 with this, the thing about the rule yard is it’s an inevitable, it is the entangled running of all
02:00:19 possible rules. So you don’t get to say, it’s not like you’re saying, which rule yard are you
02:00:25 picking? Because it’s all possible formal rules. It’s not like it’s just, well, actually, it’s
02:00:32 only footnote. The only footnote, it’s an important footnote, is it’s all possible
02:00:37 computational rules, not hyper computational rules. That is, it’s running all the rules that would be
02:00:46 accessible to a Turing machine, but it is not running all the rules that will be accessible
02:00:51 to a thing that can solve problems in finite time that would take a Turing machine infinite time to
02:00:56 solve. So you can, even Alan Turing knew this, that you could make oracles for Turing machines,
02:01:01 where you say a Turing machine can’t solve the whole thing problem for Turing machines. It can’t
02:01:05 know what will happen in any Turing machine after an infinite time, in any finite time,
02:01:10 but you could invent a box, just make a black box. You say, I’m going to sell you an oracle
02:01:15 that will just tell you, you know, press this button. It’ll tell you what the Turing machine
02:01:19 will do after an infinite time. You can imagine such a box. You can’t necessarily build one in
02:01:23 the physical universe, but you can imagine such a box. And so we could say, well, in addition to,
02:01:29 so in this Rulliad, we’re imagining that there is a computational, that at the end, it’s running
02:01:36 rules that are computational. It doesn’t have a bunch of oracle black boxes in it. You say, well,
02:01:42 why not? Well, it turns out if there are oracle black boxes, the Rulliad that is,
02:01:48 you can make a sort of super Rulliad that contains those oracle black boxes,
02:01:53 but it has a cosmological event horizon relative to the first one. They can’t communicate.
02:01:57 In other words, you can end up with, what ends up happening is it’s like in the physical universe,
02:02:06 in this causal graph that represents the causal relationships of different things,
02:02:09 you can have an event horizon where the causal graph is disconnected, where the effect here,
02:02:16 an event happening here does not affect an event happening here because there’s a disconnection
02:02:20 in the causal graph. And that’s what happens in an event horizon. And so what will happen between
02:02:26 this kind of the ordinary Rulliad and the hyper Rulliad is there is an event horizon and we,
02:02:34 in our Rulliad, will just never know that they’re just separate things. They’re not connected.
02:02:42 And maybe I’m not understanding, but just because we can’t observe it,
02:02:47 why does that mean it doesn’t exist?
02:02:49 So it might exist, but it’s not clear what it… So what, so to speak, whether it exists. What
02:02:57 we’re trying to understand is why does our universe exist? We’re not trying to ask the
02:03:01 question what… Let me say another thing. Let me make a meta comment, which is that I have not
02:03:10 thought through this hyper Rulliad business properly. So I can’t… The hyper Rulliad is
02:03:18 referring to a Rulliad in which hyper computation is possible.
02:03:22 That’s correct. Yes.
02:03:23 Okay. So the footnote to the footnote is we’re not sure why this is important.
02:03:33 Yeah, that’s right. So let’s ignore that. Okay. It’s already abstract enough. Okay. So,
02:03:39 okay. So the one question is we have to say, if we’re saying, why does the universe exist?
02:03:46 One question is why is it this universe and not another universe? Okay. So the important point
02:03:52 about this Rulliad idea is that in the Rulliad are all possible formal systems. So there’s no
02:03:59 choice being made. There’s no like, oh, we pick this particular universe and not that one. That’s
02:04:05 the first thing. The second thing is that we have to ask the question. So you say, why does two plus
02:04:12 two equals four exist? That is a thing that necessarily is that way just on the basis of
02:04:20 the meaning of the terms, two and plus and equals and so on. So the thing is that this Rulliad
02:04:27 object is in a sense a necessary object. It is just the thing that is the consequence of working
02:04:34 out the consequence of the formal definition of things. It is not a thing where you’re saying,
02:04:40 and this is picked as the particular thing. This is just something which necessarily is that thing
02:04:47 because of the definition of what it means to have computation. So the Rulliad, it’s a formal system.
02:04:54 Yes. But does it exist? Ah, well, where are we in this whole thing?
02:05:02 Yes. We are part of this Rulliad. So there is no sense to say, does two plus
02:05:10 two equals four exist? Well, in some sense, it necessarily exists. It’s a necessary object. It’s
02:05:19 not a thing that way you can ask. Usually in philosophy, there’s a sort of distinction made
02:05:25 between necessary truths, contingent truths, analytic propositions, synthetic propositions
02:05:32 that are a variety of different versions of this. They’re things which are necessarily true just
02:05:37 based on the definition of terms. And there are things which happen to be true in our universe.
02:05:42 But we don’t exist in Rullial space. That’s one of the coordinates that define our existence.
02:05:51 Well, okay. So yes, yes. But this Rulliad is the set of all possible Rullial coordinates.
02:05:58 So what we’re saying is it contains that. So what we’re saying is we exist as, okay, so
02:06:04 our perception of what’s going on is we’re at a particular place in this Rulliad,
02:06:09 and we are concluding certain things about how the universe works based on that.
02:06:13 But the question is, do we understand, you know, is there something where we say,
02:06:19 okay, so why does it work that way? Well, the answer is, I think it has to work that way,
02:06:27 because this Rulliad is a necessary object in the sense that it is a purely formal object,
02:06:35 just like 2 plus 2 equals 4. It’s not an object that was made of something. It’s an object that
02:06:41 is just an expression of the necessary collection of formal relations that exist.
02:06:46 And so then the issue is, can we, in our experience of that, is it, you know, can we have
02:06:53 tables and chairs, so to speak, in that just by virtue of our experience of that necessary thing?
02:07:00 And, you know, what people have generally thought, and I don’t know of a lot of discussion of this,
02:07:06 why does the universe exist question? It’s been a very, you know, I’ve been surprised actually at
02:07:12 how little, I mean, I think it’s one of these things that’s really kind of far out there. But
02:07:17 the thing that is, you know, the surprise here is that all possible formal rules, when you run them
02:07:25 together, and that’s the critical thing, when you run them together, they produce this kind of
02:07:30 entangled structure that has a definite structure. It’s not just, you know, a random arbitrary thing,
02:07:37 it’s a thing with definite structure. And that structure is the thing when we are embedded in
02:07:42 that structure, when anything, you know, an entity embedded in that structure perceives something,
02:07:48 which is then we can interpret as physics and things like this. So in other words, we don’t
02:07:54 have to ask the question, the why does it exist? It necessarily exists.
02:08:00 I’m missing this part. Why does it necessarily exist?
02:08:02 Okay, okay.
02:08:03 So like, you need to have it if you want to formalize the relation between entities, but
02:08:14 why do you need to have relations?
02:08:15 Okay, okay. So let’s say you say, well…
02:08:22 It’s like, why does math have to exist?
02:08:24 Fair question. Okay, fair question. Let’s see. I think the thing to think about is
02:08:33 the existence of mathematics is something where given a definition of terms,
02:08:40 what follows from that definition inevitably follows. So now you can say, why define any terms?
02:08:47 But in a sense, the, well, that’s okay. So the definition of terms, I mean, I think the way to
02:08:56 think about this, let me see.
02:08:58 So like concrete terms.
02:09:01 Well, they’re not very concrete. I mean, they’re just things like, you know, logical or.
02:09:09 Right, but that’s a thing. That’s a powerful thing.
02:09:13 Well, yes, okay. But the point is that it is not a thing of a, you know, people imagine there is,
02:09:20 I don’t know, the, you know, an elephant or something or the, you know, elephants are presumably
02:09:28 not necessary objects. They happen to exist as a result of kind of biological evolution and
02:09:34 whatever else. But the thing is that in some sense that there is, it is a different kind of thing
02:09:43 to say, does plus exist? It’s not like an elephant.
02:09:48 So a plus seems more fundamental, more basic than an elephant. Yes. But you can imagine a world
02:09:56 without plus or anything like it. Like, why do formal things that are discrete, that can be used
02:10:05 to reason have to exist?
02:10:08 Well, okay. So why? Okay. So then the question is, but the whole point is computation.
02:10:14 We can certainly imagine computation. That is, we can certainly say there is a formal system that
02:10:21 we can construct abstractly in our minds that is computation. And that’s the, you know, we can
02:10:30 imagine it. Now the question is, is it that formal system, once we exist as observers embedded in
02:10:39 that formal system, that’s enough to have something which is like our universe. And so then what
02:10:46 you’re kind of asking is perhaps is why, I mean, the point is we definitely can imagine it.
02:10:53 There’s nothing that says that we’re not saying that it’s sort of inevitable that that is a thing
02:11:02 that we can imagine. We don’t have to ask, does it exist? We’re just, it is definitely something
02:11:07 we can imagine. Now that’s, then we have this thing that is a formally constructible thing
02:11:15 that we can imagine. And now we have to ask the question, what, you know, given that formally
02:11:20 constructible thing, what is, what consequences does that, if we were to perceive that formally,
02:11:28 if we were embedded in that formally constructible thing, what would we perceive about the world?
02:11:33 And we would say, we perceive that the world exists because we are seeing all of this mechanism
02:11:40 of all these things happening. And, but that’s something that is just a feature of, it’s something
02:11:46 where we are… See, another way of asking this that I’m trying to get at, I understand why it
02:11:53 feels like this ruley ad is necessary, but maybe it’s just me being human, but it feels like then
02:12:04 you should be able to, not us, but somehow step outside of the ruley ad. Like what’s outside the
02:12:11 ruley ad? Well, the ruley ad is all formal systems. So there’s nothing because… But that’s what a
02:12:17 human would say. I know that’s what a human would say, because we’re used to the idea that there are,
02:12:22 there’s, but the whole point is that by the time it’s all possible formal systems, it’s, it’s like,
02:12:29 it is all things you can imagine, but… All computations you can imagine, but like we don’t…
02:12:36 Well, so the issue is, can we encode? Okay. So that’s a fair question. Is it possible to encode
02:12:45 all, I mean, once we, is there something that isn’t what we can represent formally?
02:12:52 Right. That is, is there something that, and that’s, I think, related to the hyper ruley ad
02:12:57 footnote, so to speak, which I’m afraid that the, you know, one of the things sort of interesting
02:13:04 about this is, you know, there has been some discussion of this in theology and things like
02:13:08 that, but, which I don’t necessarily understand all of, but the key sort of new input is this idea
02:13:19 that all possible formal systems, it’s like, you know, if you make a world, people say, well, you
02:13:25 make a world with a particular, in a particular way with particular rules, but no, you don’t do
02:13:30 that. You can make a world that deals with all possible rules, and then merely by virtue of
02:13:37 living in a particular place in that world, so to speak, we have the perception we have of what the
02:13:42 world is like. Now, I have to say the, it’s sort of interesting because I’ve, you know, I wrote this
02:13:49 piece about this, and I, you know, this philosophy stuff is not super easy, and I’ve, as I’m talking
02:13:57 to you about it, and I actually haven’t, you know, people have been interested in lots of different
02:14:00 things we’ve been doing, but this, why does the universe exist, has been, I would say, one of the,
02:14:05 one of the ones that you would think people will be most interested in, but actually, I think
02:14:10 they’re just like, oh, that’s just something complicated that, so I haven’t, I haven’t explained
02:14:17 it as much as I’ve explained a bunch of other things, and I have to say, I think I, I think I
02:14:21 may be missing a couple of pieces of that argument that would be, so it’s kind of a like…
02:14:27 Well, you are, your conscious being is computationally bounded, so you’re missing…
02:14:32 Indeed.
02:14:33 Having written quite a few articles yourself, you’re now missing some of the pieces.
02:14:38 Yes, right.
02:14:39 That’s the limitation of being human.
02:14:40 Right. One of the consequences of this, why the universe exists thing, is that you’re missing
02:14:46 something, and this kind of concept of rule adds and, you know, places in there representing our
02:14:53 perception of the universe and so on. One of the weird consequences is, if the universe exists,
02:14:59 mathematics must also exist. And that’s a weird thing, because mathematics, people have been very
02:15:06 confused, including me, have been very confused about the question of kind of what, what is the
02:15:14 definition of mathematics? What is, what kind of a thing is mathematics? Is mathematics something
02:15:20 where we just write down axioms like Euclid did for geometry, and we just build the structure,
02:15:25 and we could have written down different axioms, and we’d have a different structure? Or is it
02:15:28 something that has a more fundamental sort of truth to it? And I have to say, this is one of
02:15:33 these cases where I’ve long believed that mathematics has a great deal of arbitrariness to
02:15:38 it, that there are particular axioms that kind of got written down by the Babylonians, and, you
02:15:43 know, that’s what we’ve ended up with the mathematics that we have. And I have to say,
02:15:47 actually, my wife has been telling me for 25 years, she was a mathematician, she’s been telling me,
02:15:51 you’re wrong about the foundations of mathematics. And, you know, I’m like, no, no, no, I know what
02:15:57 I’m talking about. And finally, she’s much more right than I’ve been. So it’s one of the…
02:16:04 So, I mean, her sense and your sense, are we just, so this is to the question of metamathematics,
02:16:11 just kind of on a trajectory through ruleal space, except in mathematics, through a trajectory of
02:16:18 a certain kind of… I think that’s partly the idea. So I think that the notion is this. So 100
02:16:23 years ago, a little bit more than 100 years ago, people have been doing mathematics for ages,
02:16:28 but then in the late 1800s, people decided to try and formalize mathematics and say, you know,
02:16:34 it is mathematics is, you know, we’re going to break it down, we’re going to make it like logic,
02:16:38 make it out of sort of fundamental primitives. And that was people like Frager and Piano and
02:16:43 Hilbert and so on. And they kind of got this idea of let’s do kind of Euclid, but even better,
02:16:50 let’s just make everything just in terms of this sort of symbolic axioms, and then build
02:16:54 up mathematics from that. And that, you know, they thought at the time, as soon as they get
02:17:00 these symbolic axioms, that they made the same mistake, the kind of computational irreducibility
02:17:05 mistake. They thought as soon as we’ve written down the axioms, then we’ll just have a machine,
02:17:11 kind of a super mathematical, so to speak, that can just grind out all true theorems of mathematics.
02:17:17 That got exploited by Gödel’s theorem, which is basically the story of computational
02:17:21 irreducibility. It’s that even though you know those underlying rules, you can’t deduce all
02:17:26 the consequences in any finite way. But now the question is, okay, so they broke mathematics down
02:17:34 into these axioms, and they say now you build up from that. So what I’m increasingly coming to
02:17:40 realize is that’s similar to saying let’s take a gas and break it down into molecules. There’s gas
02:17:46 laws that are the large scale structure and so on that we humans are familiar with, and then there’s
02:17:52 the underlying molecular dynamics. And I think that the axiomatic level of mathematics, which
02:17:57 we can access with automated theorem proving and proof assistance and these kinds of things,
02:18:02 that’s the molecular dynamics of mathematics. And occasionally we see through to that molecular
02:18:07 dynamics. We see undecidability, we see other things like this. One of the things I’ve always
02:18:12 found very mysterious is that Gödel’s theorem shows that there are sort of things which cannot
02:18:18 be finitely proved in mathematics. There are proofs of arbitrary length, infinite length proofs that
02:18:23 you might need. But in practical mathematics, mathematicians don’t typically run into this.
02:18:28 They just happily go along doing their mathematics. And I think what’s actually
02:18:32 happening is that what they’re doing is they’re looking at this. They are essentially observers
02:18:38 in metamathematical space, and they are picking a reference frame in metamathematical space,
02:18:45 and they are computationally bounded observers in metamathematical space,
02:18:49 which is causing them to deduce that the laws of metamathematics and the laws of mathematics,
02:18:55 like the laws of fluid mechanics, are much more understandable than this underlying
02:19:00 molecular dynamics. And so what gets really bizarre is thinking about kind of the analogy
02:19:06 between metamathematics, this idea of you exist in this sort of space of possible,
02:19:16 in this kind of mathematical space where the individual kind of points in the mathematical
02:19:21 space are statements in mathematics, and they’re connected by proofs where one statement, you know,
02:19:27 you take a couple of different statements, you can use those to prove some other statement,
02:19:30 and you’ve got this whole network of proofs. That’s the kind of causal network of mathematics,
02:19:35 of what can prove what and so on. And you can say at any moment in the history of a mathematician,
02:19:42 of a single mathematical consciousness, you are in a single kind of slice of this
02:19:49 kind of metamathematical space. You know a certain set of mathematical statements.
02:19:54 You can then deduce with proofs, you can deduce other ones, and so on. You’re kind of gradually
02:19:58 moving through metamathematical space. And so it’s kind of the view is that the reason that
02:20:04 mathematicians perceive mathematics to have the sort of integrity and lack of kind of undecidability
02:20:10 and so on that they do is because they, like we as observers of the physical universe,
02:20:15 we have these limitations associated with computational boundedness, single thread of time,
02:20:19 consciousness limitations, basically, that the same thing is true of mathematicians perceiving
02:20:24 sort of metamathematical space. And so what’s happening is that if you look at one of these
02:20:30 formalized mathematics systems, something like Pythagoras’s theorem, it’ll take, oh, I don’t know,
02:20:37 what is it, maybe 10,000 individual little steps to prove Pythagoras’s theorem. And one of the
02:20:43 bizarre things that’s sort of an empirical fact that I’m trying to understand a little bit better,
02:20:48 if you look at different formalized mathematics systems, they actually have different axioms
02:20:54 underneath that they can all prove Pythagoras’s theorem. And so in other words, it’s a little bit
02:20:59 like what happens with gases. We can have air molecules, we can have water molecules, but they
02:21:03 still have fluid dynamics. Both of them have fluid dynamics. And so similarly, at the level that
02:21:09 mathematicians care about mathematics, it’s way above the molecular dynamics, so to speak.
02:21:14 And there are all kinds of weird things. Like, for example, one thing I was realizing recently
02:21:18 is that the quantum theory of mathematics, that’s a very bizarre idea. But basically,
02:21:23 when you prove what is a proof is you’ve got one statement in mathematics, you go through
02:21:29 other statements, you eventually get to a statement you’re trying to prove, for example,
02:21:32 that’s a path in metamathematical space. And that’s a single path, a single proof is a single
02:21:38 path. But you can imagine there are other proofs of the same result. There are a bundle of proofs.
02:21:44 There’s this whole set of possible proofs. Yeah, you could think of it as branching,
02:21:48 similar to the quantum mechanics model that you were talking about. Exactly. And then there’s
02:21:52 some invariance that you can formalize in the same way that you can for the quantum mechanical.
02:21:56 Right. So the question is, in proof space, as you start thinking about multiple proofs,
02:22:01 are there analogs of, for example, destructive interference of multiple proofs? So here’s a
02:22:05 bizarre idea that’s just a couple of days old, so not yet fully formed. But as you try and do that,
02:22:12 when you have two different proofs, it’s like two photons going in different directions,
02:22:16 you have two proofs, which at an intermediate stage are incompatible. And that’s kind of like
02:22:20 destructive interference. Is it possible for this to instruct the engineering of automated proof
02:22:26 systems? Absolutely. I mean, as a practical matter, I mean, you know, this whole question,
02:22:31 in fact, Jonathan Gorod has a nice heuristic for automated theorem provers that’s based on
02:22:36 our physics project that is looking for essentially using kind of using energy in our
02:22:44 models. Energy is kind of level of activity in this hypergraph. And so it’s sort of a heuristic
02:22:51 for automated theorem proving about how do you pick which path to go down that is based on
02:22:57 essentially physics. And I mean, the thing that gets interesting about this is the way that one
02:23:03 can sort of have the interplay between, like, for example, a black hole. What is a black hole
02:23:07 in metamathematics? So the answer is, what is black hole in physics? A black hole in physics
02:23:12 is where in the simplest form of black hole time ends. That is all, you know, everything is crunched
02:23:19 down to the space time singularity, and everything just ends up at that singularity. So in our
02:23:24 models, and that’s a little hard to understand in general relativity with continuous mathematics,
02:23:29 and what does singularity look like? In our models, it’s something very pragmatic. It’s just,
02:23:33 you’re applying these rules, time is moving forward. And then there comes a moment where
02:23:37 the rules, no rules apply. So time stops. It’s kind of like the universe dies, that, you know,
02:23:43 that nothing happens in the universe anymore. Well, in mathematics, that’s a decidable theory.
02:23:49 That’s a theory. So theories which have undecidability, which are things like
02:23:53 arithmetic, set theory, all the serious models, theories in mathematics, they all have the feature
02:23:58 that there are proofs of arbitrarily long length. In something like Boolean algebra,
02:24:02 which is a decidable theory, there are, you know, any question in Boolean algebra, you can just go
02:24:07 crunch, crunch, crunch, and in a known number of steps, you can answer it. You know, satisfiability,
02:24:13 you know, might be hard, but it’s still a bounded number of steps to answer any satisfiability
02:24:17 problem. And so that’s the notion of a black hole in physics where time stops. That’s analogous to
02:24:26 in mathematics where there aren’t infinite length proofs, where when in physics, you know, you can
02:24:32 wander around the universe forever if you don’t run into a black hole. If you run into a black
02:24:36 hole and time stops, you’re done. And it’s the same thing in mathematics between decidable
02:24:41 theories and undecidable theories. That’s an example. And I think where sort of the attempt
02:24:47 to understand, so another question is kind of what is the general activity of metamathematics?
02:24:54 What is the bulk theory of metamathematics? So in the literature of mathematics, there are about
02:24:59 three million theorems that people have published. And those represent, it’s kind of on this, it’s
02:25:05 like on the earth, we would be, you know, we’ve put cities in particular places on the earth,
02:25:11 but yet there is ultimately, you know, we know the earth is roughly spherical,
02:25:15 and there’s an underlying space. And we could just talk about, you know, the world of space
02:25:20 in terms of where our cities happen to be, but there’s actually an underlying space. And so the
02:25:24 question is, what’s that for metamathematics? And as we kind of explore what is, for example,
02:25:29 for mathematics, which is always likes taking sort of abstract limits. So an obvious abstract
02:25:34 limit for mathematics to take is the limit of the future of mathematics. That is, what will be,
02:25:40 you know, the ultimate structure of mathematics. And one of the things that’s an empirical
02:25:44 observation about mathematics that’s quite interesting is that a lot of theories in one
02:25:49 area of mathematics, algebraic geometry or something, might have, they play into another area
02:25:54 of mathematics. That same kind of fundamental construct seemed to occur in very different
02:26:00 areas of mathematics. And that’s structurally captured a bit with category theory and things
02:26:04 like that. But I think that there’s probably an understanding of this metamathematical space that
02:26:09 will explain why different areas of mathematics ultimately sort of map into the same thing.
02:26:15 And I mean, you know, my little challenge to myself is what’s time dilation in metamathematics?
02:26:21 In other words, as you basically, as you move around in this mathematical space of possible
02:26:27 statements, you know, how does that moving around? It’s basically what’s happening is
02:26:33 that as you move around in the space of mathematical statements, it’s like you’re
02:26:36 changing from algebra to geometry to whatever else. And you’re trying to prove the same theorem.
02:26:42 But as you try, if you keep on moving to these different places, it’s slower to prove that
02:26:46 theorem because you keep on having to translate what you’re doing back to where you started from.
02:26:50 And that’s kind of the beginnings of the analog of time dilation in metamathematics.
02:26:54 Plus, there’s probably fractional dimensions in this space as well.
02:26:58 Oh, this space is a very messy space. This space is much messier than physical space. I mean,
02:27:02 even in the models of physics, physical space is very tame compared to branchial space and
02:27:09 ruleal space. I mean, the mathematical structure, you know, branchial space is probably more like
02:27:14 Hilbert space, but it’s a rather complicated Hilbert space. And ruleal space is more like
02:27:20 this weird infinity groupoid story of Grothendieck. And, you know, I can explain that a little bit
02:27:25 because in metamathematical space, a path in metamathematical space is a path between two
02:27:34 statements is a way to get by proofs, is a way to find a proof that goes from one statement to
02:27:39 another. And so one of the things you can do, you can think about is between statements, you’ve got
02:27:45 proofs and they are paths between statements. Okay, so now you can go to the next level and you
02:27:50 can ask, what about a mapping from one proof to another? And so that’s in category theory,
02:27:56 that’s kind of a higher category, the notion of higher categories where you’re mapping not just
02:28:03 between objects, but you’re mapping between the mappings between objects and so on.
02:28:07 And so you can keep doing that. You keep saying higher order proofs. I want mappings between
02:28:12 proofs between proofs and so on. And that limiting structure, oh, by the way, one thing that’s very
02:28:17 interesting is imagine in proof space, you’ve got these two proofs. And the question is,
02:28:22 what is the topology of proof space? In other words, if you take these two paths,
02:28:26 can you continuously deform them into each other? Or is there some big hole in the middle that
02:28:31 prevents you from continuously deforming them one into the other? It’s kind of like, you know,
02:28:35 when you think about some, I don’t know, some puzzle, for example, you’re moving pieces around
02:28:39 on some puzzle, and you can think about the space of possible states of the puzzle.
02:28:44 And you can make this graph that shows from one state of the puzzle to another state of
02:28:47 the puzzle and so on. And sometimes you can easily get from one state to any other state,
02:28:52 but sometimes there’ll be a hole in that space. And there’ll be, you know, you always have to
02:28:56 go around the circuitous route to get from here to there. There won’t be any direct way.
02:29:01 That’s kind of a question of whether there’s sort of an obstruction in the space. And so the question
02:29:07 is in proof space, what is the, what are, you know, what does it mean if there’s an obstruction in proof
02:29:14 space? Yeah, I don’t even know what an obstruction means in proof space because for it to be an
02:29:19 obstruction, it should be reachable some other way from some other place, right? So this is like
02:29:25 an unreachable part of the graph. No, it’s not just an unreachable part. It’s a part where
02:29:30 there are paths that go one way, there are paths that go the other way. And this question of
02:29:34 homotopy in mathematics is this question, can you continuously deform, you know, from one path to
02:29:39 another path or do you have to go in a jump, so to speak? So it’s like if you’re going around a
02:29:44 sphere, for example, if you’re going around, I don’t know, a cylinder or something, you can
02:29:48 wind around one way and you can, there’s no paths where you can easily deform one path into another
02:29:55 because it’s just sort of sitting on the same side of the cylinder. But when you’ve got something
02:29:58 that winds all the way around a cylinder, you can’t continuously deform that down to a point
02:30:03 because it’s, it’s stuck wrapped around. My intuition about proof spaces, you should be
02:30:07 able to deform it. I mean that because then otherwise it doesn’t even make sense because
02:30:11 if the topology matters of the way you move about the space that I don’t even know what that means.
02:30:17 Well, what it would mean is that you would have one way of doing a proof of something over here
02:30:22 in algebra and another way of doing a proof of something over here in geometry. And there would
02:30:27 not be an intermediate way to map between those proofs. How would that be possible if they started
02:30:32 the same place and ended the same place? Well, it’s the same thing as, you know,
02:30:37 we’ve got points on a, you know, if we’ve got paths on a cylinder.
02:30:40 Now I understand how it works in physical space, but it just doesn’t,
02:30:44 it feels like proof space shouldn’t have that. Okay. I mean,
02:30:47 I’m not sure. I don’t know. We’ll know very soon because we get to do some experiments. This is
02:30:52 the great thing about this stuff is that in fact, you know, in the next few days,
02:30:56 I hope to do a bunch of experiments on this. So you’re playing like proofs in this kind of space.
02:31:01 Yes. Yes. I mean, so, you know, this is toy, you know, theories and, you know, we’ve got
02:31:07 good. So this kind of segues to perhaps another thing, which is this whole idea of multi computation.
02:31:13 So this is another kind of bigger idea that, so, okay, this has to do with how do you make models
02:31:21 of things? And it’s going to, so I’ve sort of claimed that there’ve been sort of four epochs
02:31:28 in the history of making models of things. And this multi computation thing is the fourth,
02:31:35 is a new epoch. What are the first three? The first one is back in antiquity, ancient Greek
02:31:41 times. People were like, what’s the universe made of? Oh, it’s made of, you know, everything is
02:31:46 water, Thales, you know, or everything is made of atoms. It’s sort of, what are things made of?
02:31:52 Or the, you know, there are these crystal spheres that represent where the planets are and so on.
02:31:58 It’s like a structural idea of how the universe is constructed. There’s no real notion of dynamics.
02:32:03 It’s just, what is the universe? How is the universe made? Then we get to the 1600s and we
02:32:08 get to the sort of revolution of mathematics being introduced into physics. And then we have this
02:32:14 kind of idea of you write down some equation. The, what happens in the universe is the solving of
02:32:21 that equation. Time enters, but it’s usually just a parameter. We just can, you know, sort of slide
02:32:26 it back and forth and say, here’s where it is. Okay. Then we come to this kind of computational
02:32:32 idea that I kind of started really pushing in the early 1980s as a result, you know,
02:32:39 the things that we were talking about before about complexity, that was my motivation. But
02:32:43 the bigger story was the story of kind of computational models of things. And the big
02:32:48 difference there from the mathematical models is, in mathematical models, there’s an equation,
02:32:52 you solve it, you kind of slide time to the place where you want it. In computational models,
02:32:58 you give the rule and then you just say, go run the rule. And time is not something you get to
02:33:04 slide. Time is something where it just, you run the rule, time goes in steps. And that’s how you
02:33:11 work out how the system behaves. You don’t, time is not just a parameter. Time is something that
02:33:16 is about the running of these rules. And so there’s this computational irreducibility. You can’t jump
02:33:21 ahead in time. But there’s still, important thing is there’s still one thread of time. It’s still
02:33:27 the case, you know, the cellular automaton state, then it has the next state and the next state and
02:33:31 so on. The thing that is kind of, we’ve sort of tipped off by quantum mechanics in a sense,
02:33:36 although it actually feeds back even into relativity and things like that, that there’s
02:33:41 these multiple threads of time. And so in this multi computation paradigm, the kind of idea is,
02:33:47 instead of there being the single thread of time, there are these kind of distributed asynchronous
02:33:52 threads of time that are happening. And the thing that’s sort of different there is if you want to
02:33:57 know what happened, if you say what happened in the system, in the case of the computational
02:34:02 paradigm, you just say, well, after a thousand steps, we got this result, right? But in the
02:34:08 multi computational paradigm, after a thousand steps, not even clear what a thousand steps means,
02:34:13 because you’ve got all these different threads of time, but there is no state. There’s all these
02:34:17 different possible, you know, there’s all these different paths. And so the only way you can know
02:34:22 what happened is to have some kind of observer who is saying, here’s how to parse the results
02:34:27 of what was going on. Right. But that observer is embedded and they don’t have a complete picture.
02:34:31 So in the case of physics, that’s right. Yes. And then in the, but that’s, but so the idea is
02:34:37 that in this multi computation setup, that it’s this idea of these multiple threads of time
02:34:42 and models that are based on that. And this is similar to what people think about in
02:34:47 non deterministic computation. So you have a Turing machine. Usually it has a definite state. It
02:34:52 follows another state, follows another state. But typically what people have done when they
02:34:56 thought about these kinds of things is they’ve said, well, there are all these possible paths,
02:34:59 and non deterministic Turing machine can follow all these possible paths, but we just want one
02:35:04 of them. We just want the one that’s the winner that factors the number or whatever else. And
02:35:08 similarly, it’s the same story in logic programming and so on, but we say, we’ve got this goal,
02:35:13 find us a path to that goal. I just want one path, then I’m happy. Or theorem proving,
02:35:18 same story. I just want one proof and then I’m happy. What’s happening in multi computation
02:35:23 in physics is we actually care about many paths. And well, there is a case, for example, probabilistic
02:35:29 programming is a version of multi computation in which you’re looking at all the paths. You’re just
02:35:33 asking for probabilities of things. But in a sense in physics, we’re taking different kinds of
02:35:39 samplings. For example, in quantum mechanics, we’re taking a different kind of sampling
02:35:43 of all these multiple paths. But the thing that is notable is that when you’re an observer embedded
02:35:51 in this thing, et cetera, et cetera, et cetera, with various other sort of footnotes and so on,
02:35:56 it is inevitable that the thing that you parse out of the system looks like general relativity
02:36:02 and quantum mechanics. In other words, that just by the very structure of this multi computational
02:36:07 setup, it inevitably is the case that you have certain emergent laws. Now, why is this perhaps
02:36:16 not surprising? In thermodynamics and statistical mechanics, there are sort of inevitable emergent
02:36:21 laws of sort of gas dynamics that are independent of the details of the molecular dynamics,
02:36:28 sort of the same kind of thing. But I think what happens is what’s a sort of a funny thing that I
02:36:33 just been understanding very recently is when when I kind of introduced this whole sort of
02:36:39 computational paradigm complexity ish thing back in the 80s, it was kind of like a big downer
02:36:44 because it’s like there’s a lot of stuff you can’t say about what systems will do.
02:36:48 And then what I realized is and then you might say, now we’ve got multi computation, it’s even
02:36:52 worse. You know, it isn’t just one thread of time that we can’t explain. It’s all these threads of
02:36:56 time. It can’t explain anything. But the following thing happens because there is all this
02:37:03 irreducibility and any detailed thing you might want to answer, it’s very hard to answer. But
02:37:08 when you have an observer who has certain characteristics like computational boundedness,
02:37:13 sequentiality of time and so on, that observer only samples certain aspects of this incredible
02:37:19 complexity going on in this multi computational system. And that observer is sensitive only to
02:37:25 to some underlying core structure of this multi computational system. There is all this
02:37:30 irreducible computation going on, all these details. But to that kind of observer, what’s
02:37:36 important is only the core structure of multi computation, which means that observer
02:37:41 observes comparatively simple laws. And I think it is inevitable that that observer
02:37:47 observes laws which are mathematically structured like general relativity and quantum
02:37:51 mechanics, which, by the way, are the same law in our in our model of physics.
02:37:56 So that’s an explanation why there are simple laws that explain a lot for this observer.
02:38:01 Potentially, yes. But what the place where this gets really interesting is there are all these
02:38:07 fields of science where people have kind of gotten stuck, where they say we’d really love to
02:38:12 have a physics like theory of economics. We’d really love to have a physics like law and
02:38:16 linguistics. You got to talk about molecular biology here. OK, so where where where does
02:38:22 multi computation come in for biology? Economics is super interesting, too, but biology. OK,
02:38:27 let’s talk about that. So let’s talk about chemistry for a second. OK, so I mean, I have
02:38:31 to say, you know, this is it’s such a weird business for me because, you know, there are
02:38:35 these kind of paradigmatic ideas and then the actual applications. And it’s like I’ve always
02:38:39 said, I know nothing about chemistry. I learned all the chemistry I know, you know, the night
02:38:43 before some exam when I was 14 years old. But I’ve actually learned a bunch more chemistry.
02:38:47 And in Wolfram language these days, we have really pretty nice symbolic representation
02:38:51 of chemistry. And in understanding the design of that, I’ve actually, I think, learned a certain
02:38:55 amount of chemistry. So if you quizzed me on sort of basic high school chemistry, I would
02:38:59 probably totally fail. But but but OK, so what is chemistry? I mean, chemistry is sort of a
02:39:06 story of, you know, chemical reactions are like you’ve got this particular chemical that’s
02:39:11 represented as some graph of, you know, these are these are this configuration of molecules
02:39:15 with these bonds and so on. And a chemical reaction happens. You’ve got these sort of
02:39:20 two graphs. They interact in some way. You’ve got another graph or multiple other graphs
02:39:24 out. So that’s kind of the sort of the the abstract view of what’s happening in chemistry.
02:39:30 And so when you do a chemical synthesis, for example, you are given certain sort of these
02:39:36 are possible reactions that can happen. And you’re asked, can you piece together this
02:39:40 sequence of such reactions, a sequence of such sort of axiomatic reactions usually called name
02:39:45 reactions in chemistry? Can you piece together a sequence of these reactions so that you get out
02:39:50 at the end this great molecule you were trying to synthesize? And so that’s a story very much
02:39:55 like theorem proving. And people have done actually they start in the 1960s looking at
02:40:00 kind of the theorem proving approach to that, although it didn’t really it didn’t it didn’t
02:40:04 was sort of done too early, I think. But anyway, so that’s kind of the view is that that chemistry,
02:40:09 chemical reactions are the story of of all these different sort of paths of possible things that
02:40:15 go on. OK, let’s let’s go to an even lower level. Let’s say instead of asking about which species
02:40:22 of molecules we’re talking about, let’s look at individual molecules and let’s say we’re looking
02:40:26 at individual molecules and they are having chemical reactions and we’re building up this
02:40:31 big graph of all these reactions that are happening. OK, so so then we’ve got this big
02:40:36 graph. And by the way, that big graph is incredibly similar to this hypergraph rewriting things.
02:40:42 In fact, in the underlying theory of multi computation there, these things we call token
02:40:46 event graphs, which are basically you’ve broken your state into tokens. Like in the case of a
02:40:52 hypergraph, you’ve broken it into hyper edges and each event is just consuming some number of tokens
02:40:58 and producing some number of tokens. But then you have to there’s a lot of work to be done
02:41:02 on update rules in terms of what they actually are for chemistry. Yeah, what they offer are
02:41:08 observed chemistry. Yes, indeed. Yes, indeed. And we’ve been working on that actually because we
02:41:12 have this beautiful system and Wolfram language for representing chemistry symbolically. So we
02:41:17 actually have you know, this is this is an ongoing thing to actually figure out what they are for
02:41:21 some practical cases. Does that require human injection or can it be automatically discovered
02:41:27 these update rules? Well, if we can do chemistry better, we could probably discover them
02:41:30 automatically. But I think in, in reality, right now, it’s like there are these particular
02:41:35 reactions. And really, to understand what’s going on, we’re probably going to pick a particular
02:41:39 subtype of chemistry. And just because because let me explain where this is going to the place
02:41:45 that his his where this is going. So got this whole network of all these molecules,
02:41:50 having all these reactions and so on. And this is some whole multi computational story because each
02:41:56 each sort of chemical reaction event is its own separate event. We’re saying they will happen
02:42:02 asynchronously. We’re not describing in what order they happen. You know, maybe that order is governed
02:42:07 by some quantum mechanics thing doesn’t really matter. We’re just saying they happen in some
02:42:11 order. And then we ask, what is the what what’s the you know, how do we think about the system?
02:42:16 Well, this thing is some kind of big multi computational system. The question is what is
02:42:21 the chemical observer? And one possible chemical observer is all you care about is did you make
02:42:27 that particular drug molecule? You’re just asking, you know, the for the one path. Another thing you
02:42:31 might care about is I want to know the concentration of each species. I want to know,
02:42:36 you know, at every stage, I’m going to solve the differential equations that represent the
02:42:40 concentrations. And I want to know what those all are. But there’s more. Because when and it’s kind
02:42:46 of like you’re going below and statistical mechanics, there’s kind of all these molecules
02:42:51 bouncing around. And you might say, we’re just going to ignore we’re just going to look at the
02:42:57 aggregate densities of certain kinds of molecules. But you can look at a lower level, you can look
02:43:02 at this whole graph of possible interactions. And so the kind of the idea would be what, you know,
02:43:08 is the only chemical observer, one who just cares about overall concentrations? Or can there be a
02:43:14 chemical observer who cares about this network of what happened? And so that the question then is,
02:43:20 so let me give an analogy. So this is where I think this is potentially very relevant to molecular
02:43:25 biology and molecular computing. When we think about a computation, usually, we say it’s input,
02:43:32 it’s output, we, you know, or chemistry, we say there’s this input, we’re going to make this
02:43:36 molecule as the output. But what if what we actually encode, what if our computation, what
02:43:42 thing we care about is some part of this dynamic network? What if it isn’t just the input and the
02:43:48 output that we care about? What if there’s some dynamics of the network that we care about? Now,
02:43:52 imagine you’re a chemical observer, what is a chemical observer? Well, in molecular biology,
02:43:57 there are all kinds of weird sorts of observers, there are membranes that exist, that have, you
02:44:03 know, different kinds of molecules that can bind to them, things like this, it’s not obvious that
02:44:08 the from a human scale, we just measure the concentration of something is the relevant story.
02:44:13 We can imagine that, for example, when we look at this whole network of possible reactions,
02:44:18 we can imagine, you know, at a physical level, we can imagine, well, what was the actual momentum
02:44:22 direction of that of that molecule? What was it which we don’t pay any attention to when we’re
02:44:26 just talking about chemical concentrations? What was the orientation of that molecule,
02:44:31 these kinds of things? And so here’s the place where I’m, I have a little suspicion, okay? So
02:44:36 one of the questions in biology is what matters in biology? And that is, you know, we have all
02:44:41 these chemical reactions, we have all these, all these molecular processes going on in, you know,
02:44:46 in biological systems, what matters? And, you know, one of the things is to be able to tell
02:44:52 what matters, well, so a big story of the what matters question was what happened in genetics
02:44:57 in 1953, when DNA, when it was figured out how DNA worked. Because before that time, you know,
02:45:03 genetics have been all these different effects and complicated things. And then it was realized,
02:45:07 ah, there’s something new, a molecule can store information, which wasn’t obvious before that
02:45:12 time, a single molecule can store information. So there’s a place where there can be something
02:45:17 important that’s happening in molecular biology, and it’s just in the sequence that’s storing
02:45:21 information in a molecule. So the possibility now is imagine this dynamic network, this, you know,
02:45:28 causal graphs and multiway causal graphs and so on, that represent all of these different reactions
02:45:33 between molecules. What if there is some aspect of that, that is storing information that’s relevant
02:45:39 for molecular biology? And the dynamic aspect of that. Yes, that’s right. So that it’s similar to
02:45:45 how the structure of a DNA molecule stores information, it could be the dynamics of the
02:45:50 system somehow stores information. And this kind of process might allow you to give predictions
02:45:56 of what that would be. Well, yes, but also imagine that you’re trying to do, for example, imagine
02:46:03 you’re trying to do molecular computation. Okay. You might think the way we’re going to do molecular
02:46:08 computation is we’re just going to run the thing. We’re going to see what came out. We’re going to
02:46:11 see what molecule came out. This is saying that’s not the only thing you can do. There is a different
02:46:16 kind of chemical observer that you can imagine constructing, which is somehow sensitive to this
02:46:22 dynamic network. Exactly how that works, how we make that measurement, I don’t know, but a few
02:46:27 ideas, but that’s what’s important, so to speak. And that means, and by the way, you can do the
02:46:33 same thing even for Turing machines. You can say, if you have a multiway Turing machine, you can say,
02:46:39 how do you compute with a multiway Turing machine? You can’t say, well, we’ve got this input and this
02:46:43 output because the thing has all these threads of time and it’s got lots of outputs. And so then you
02:46:48 say, well, what does it even mean to be a universal multiway Turing machine? I don’t fully know the
02:46:53 answer to that. It’s an interesting idea. It would freak Turing out for sure, because then the
02:46:59 dynamics of the trajectory of the computation matters. Yes. Yes. I mean, but the thing is
02:47:05 that that, so this is again, a story of what’s the observer, so to speak. In chemistry, what’s
02:47:10 the observer there? Now to give an example of where that might matter, a very sort of present
02:47:16 day example is in immunology, where we have whatever it is, 10 billion different kinds of
02:47:23 antibodies that are all these different shapes and so on. We have a trillion different kinds of T
02:47:29 cell receptors that we produce. And the traditional theory of immunology is this clonal
02:47:37 selection theory where we are constantly producing, randomly producing all these different antibodies.
02:47:42 And as soon as one of them binds to an antigen, then that one gets amplified and we produce more
02:47:46 of that antibody and so on. Back in the 1960s, an immunologist called Nils Joerner, who was the guy
02:47:53 who invented monoclonal antibodies, various other things, kind of had this network theory of the
02:47:59 immune system where it would be like, well, we produce antibodies, but then we produce antibodies
02:48:04 to the antibodies, anti antibodies, and we produce anti anti antibodies. And we get this whole dynamic
02:48:09 network of interactions between different immune system cells. And that was kind of a qualitative
02:48:16 theory at that time. And I’ve been a little disappointed because I’ve been studying immunology
02:48:21 a bit recently. And I knew something about this like 35 years ago or something. And I knew,
02:48:26 you know, I’d read a bunch of the books and I talked to a bunch of the people and so on.
02:48:29 And it was like an emerging theoretical immunology world. And then I look at the books now,
02:48:35 and they’re very thick because they’ve got, you know, there’s just a ton known about immunology
02:48:39 and, you know, all these different pathways, all these different details and so on.
02:48:43 But the theoretical sections seem to have shrunk. And so it’s so the question is, what, you know,
02:48:51 for example, immune memory, where is the where does the immune memory reside? Is it actually
02:48:55 some cells sitting in our bone marrow that is, you know, living for the whole of our lives that’s
02:48:59 going to spring into action as soon as we’re shown the same antigen? Or is it something different
02:49:05 from that? Is it something more dynamic? Is it something more like some network of interactions
02:49:09 between these different kinds of immune system cells and so on? And it’s known that there are
02:49:14 plenty of interactions between T cells and, you know, there’s plenty of dynamics. But what the
02:49:19 consequence of that dynamics is, is not clear. And to have a qualitative theory for that doesn’t
02:49:25 seem to exist. In fact, I was just been trying to study this. So I’m quite incomplete in my study
02:49:30 of these things. But I was a little bit taken aback because I’ve been looking at these things
02:49:34 and it’s like, and then they get to the end where they have the most advanced theory that they’ve
02:49:37 got. And it turns out it’s a cellular automaton theory. It’s like, okay, well, at least I understand
02:49:43 that theory. But but, you know, I think that the possibility is that in that this is a place where
02:49:52 if you want to know, you know, explain roughly how the immune system works, it ends up being
02:49:56 this sort of dynamic network. And then the the, you know, the immune consciousness, so to speak,
02:50:02 the observer ends up being something that, you know, in the end, it’s kind of like, does the
02:50:06 human get sick or whatever? But it’s a it’s something which is a complicated story that
02:50:12 relates to this whole sort of dynamic network and so on. And I think that’s another place where this
02:50:16 kind of notion of where I think multi computation has the possibility. See, one of the things, okay,
02:50:23 you can end up with something where yes, there is a general relativity in there. But it turns up,
02:50:27 but it may turn out that the observer who sees general relativity in the immune system is an
02:50:33 observer that’s irrelevant to what we care about about the immune system. I mean, it could be yes,
02:50:37 there is some effect where, you know, there’s some, you know, time dilation of T cells interacting
02:50:43 with whatever. But it’s like, that’s an effect that’s just irrelevant. And the thing we actually
02:50:47 care about is things about, you know, what happens when you have a vaccine that goes into some place
02:50:52 in shapespace? And, you know, how does that affect other places in shapespace? And how does that spread?
02:50:57 You know, what’s the what’s the analog of the speed of light in shapespace, for example, that’s an
02:51:01 that’s an important issue. If you have one of these dynamic theories, it’s like, you know, you
02:51:06 you’re poking to shapespace by having, you know, let’s say, a vaccine or something that has a
02:51:10 particular configuration in shapespace. How, how quickly as this dynamic network spreads out, how
02:51:16 quickly do you get sort of other antibodies in different places in shapespace, things like that?
02:51:22 When you say shapespace, you mean the shape of the molecules? And then, so this is like,
02:51:27 could be deeply connected to the protein and multi protein folding, all of that kind of stuff.
02:51:32 To be able to say something interesting about the the dance of proteins that
02:51:36 Right, exactly.
02:51:36 then actually has an impact on helping develop drugs, for example, or has an impact on
02:51:44 virology, immunology, helping.
02:51:46 Well, I think the big thing is, you know, when we think about molecular biology, the you know,
02:51:54 what, what is the qualitative way to think about it? You know, in other words, is it chemical
02:51:58 reaction networks? Is it, you know, genetics, you know, DNA, big, you know, big news, it’s kind of
02:52:05 there’s a digital aspect to the whole thing. You know, what is the qualitative way to think about
02:52:10 how things work in biology? You know, when we think about, I don’t know, some phenomenon like
02:52:15 aging or something, which is a big, complicated phenomenon, which just seems to have all these
02:52:18 different tentacles. Is it really the case that that can be thought about in some, you know,
02:52:23 without DNA, when people were describing, you know, genetic phenomena, there were, you know,
02:52:29 dominant recessive, this, that and the other got very, very complicated. And then people realize,
02:52:33 oh, it’s just, you know, and what is a gene and so on and so on and so on. Then people realize
02:52:38 it’s just base pairs. And there’s this digital representation. And so the question is, what is
02:52:42 the overarching representation that we can now start to think about using a molecular biology?
02:52:47 I don’t know how this will work out. And this is again, one of these things where, and the place
02:52:51 where that gets important is, you know, maybe molecular biology is doing molecular computing
02:52:58 by using some dynamic process that is something where it is very happily saying, oh, I just got
02:53:03 a result. It’s in the dynamic structure of this network. Now I’m going to go and do some other
02:53:07 thing based on that result, for example. But we’re like, oh, I don’t know what’s going on. You know,
02:53:12 it’s just, we just measured the levels of these chemicals and we couldn’t conclude anything.
02:53:17 But it just, we’re looking at the wrong thing. And so that’s the, that’s kind of the potential
02:53:22 there. And it’s, I mean, these things are, I don’t know, it’s for me, it’s like, I’ve not really,
02:53:30 that was not a view. I mean, I’ve thought about molecular computing for ages and ages and ages.
02:53:34 And I’ve always imagined that the big story is kind of the original promise of nanotechnology
02:53:40 of like, can we make a molecular scale constructor that will just build a molecule in any shape?
02:53:45 I don’t think I’m now increasingly concluding that’s not the big point. The big point is
02:53:50 something more dynamic. That will be an interesting endpoint for any of these things. But that’s
02:53:56 perhaps not the thing, you know, because the one example we have in molecular computing
02:54:00 that’s really working is us biological organisms. And, you know, maybe the thing that’s important
02:54:05 there is not this, you know, what chemicals do you make, so to speak, but more this kind of
02:54:10 dynamic process. The dynamic process. And then you can have a good model like the hypergraph to then
02:54:15 explore what, like simulate again, make predictions. And if they, I think just have a way to reason
02:54:22 about biology. I mean, it’s hard, you know, but first of all, biology doesn’t have theories like
02:54:28 physics. You know, physics is a much more successful sort of global theory kind of area.
02:54:34 You know, biology, what are the global theories of biology? Pretty much Darwinian evolution. That’s
02:54:39 the only global theory of biology. You know, are there any other theories just say, well,
02:54:43 the kidneys work this way, this thing works this way and so on. There isn’t, I suppose,
02:54:47 another global theory is digital information in DNA. That’s another sort of global fact about
02:54:52 biology. But the difficult thing to do is to match something you have a model of in the hypergraph
02:55:00 to the actual, like how do you discover the theory? How do you discover the theory? Okay,
02:55:05 you have something that looks nice and makes sense, but like you have to match it to validation.
02:55:10 Oh, sure. Right. And that’s tricky because you’re walking around in the dark.
02:55:15 Not entirely. I mean, so, you know, for example, in what we’ve been trying to think about is
02:55:20 take actual chemical reactions. Okay. So, you know, one of my goals is can I compute the primes
02:55:26 with molecules? Okay. If I can do that, then I kind of, maybe I can compute things. And, you know,
02:55:33 there’s this nice automated lab, these guys, these Emerald Cloud Lab people have built with
02:55:37 Wolfram language and so on. That’s an actual physical lab and you send it a piece of Wolfram
02:55:42 language code and it goes and, you know, actually does physical experiments. And so one of my goals,
02:55:47 because I’m not a test tube kind of guy, I’m more of a software kind of person, is can I make
02:55:52 something where, you know, in this automated lab, we can actually get it so that there’s some gel
02:55:57 that we made and, you know, the positions of the stripes are the primes. I love it. Yeah.
02:56:02 I mean, that would be an example of where, and that would be with a particular, you know,
02:56:08 framework for actually doing the molecular computing, you know, with particular kinds
02:56:13 of molecules. And there’s a lot of kind of ambient technological mess, so to speak,
02:56:18 associated with, oh, is it carbon? Is it this? Is it that? You know, is it important that there’s
02:56:22 a bromine atom here, et cetera, et cetera, et cetera. This is all chemistry that I don’t know
02:56:26 much about. And, you know, that’s a sort of, you know, unfortunately that’s down at the level,
02:56:32 you know, I would like to be at the software level, not at the level of the transistors,
02:56:36 so to speak. But in chemistry, you know, there’s a certain amount we have to do, I think, at the
02:56:40 level of transistors before we get up to being able to do it. Although, you know, the automated
02:56:45 labs certainly help in setting that up. I talked to a guy named Charles Hoskinson.
02:56:52 He mentioned that he’s collaborating with you. He’s an interesting guy. He sends me papers on
02:56:58 speaking of automated theorem proving a lot. He’s exceptionally well read on that area as well.
02:57:04 So what’s the nature of your collaboration with him? He’s the creator of Cardano.
02:57:08 What’s the nature of the collaboration between Cardano and the whole space of blockchain and
02:57:13 Wolfram, Wolfram Alpha, Wolfram blockchain, all that kind of stuff? Well, OK, we’re segueing to a
02:57:20 slightly different world. But so although not completely unconnected. Right. The whole thing
02:57:26 is somehow connected. I know. I mean, you know, the strange thing in my life is I’ve sort of
02:57:31 alternated between doing basic science and doing technology about five times in my life so far.
02:57:36 And the thing that’s just crazy about it is, you know, every time I do one of these alternations,
02:57:42 I think there’s not going to be a way back to the other thing. And like I thought for this
02:57:46 physics project, I thought, you know, we’re doing fundamental theory of physics. Maybe it’ll have
02:57:50 an application in 200 years. But now I’ve realized actually this multi computation idea is is
02:57:57 applicable here now. It’s and in fact, it’s also giving us this way. I’ll just mention one other
02:58:03 thing and then talk about blockchain. The the question of actually that relates to several
02:58:11 different things. But but one of the things about about OK, so our Wolfram language, which is our
02:58:18 attempt to kind of represent everything in the world computationally. And it’s the thing I kind
02:58:23 of started building 40 years ago in the form of actual Wolfram language 35 years ago. It’s kind
02:58:29 of this idea of can we can we express things about the world in computational terms? And, you know,
02:58:37 we’ve come a long way in being able to do that. Wolfram Alpha is kind of the consumer version of
02:58:42 that where you’re just using natural language as input. The and it turns it into our symbolic
02:58:46 language. And that’s, you know, the symbolic language Wolfram language is what people use
02:58:51 and have been using for the last 33 years. Actually, Mathematica, which is its first
02:58:56 instantiation, will be one third of a century old in in October. And that it’s it’s kind of
02:59:05 interesting. What do you mean one third of a century? I mean, 33 or 30? What are we? 33 and a
02:59:09 third. 33 and a third. So I’ve never heard of anyone celebrating that anniversary, but I like
02:59:17 it. I know. A third of a century, though, it’s it’s kind of get many, many slices of a century
02:59:22 that are interesting. But but, you know, I think that the the thing that’s really striking about
02:59:26 that is that means, you know, including the whole sort of technology stack I built around that’s
02:59:30 about 40 years old. And that means it’s a significant fraction of the total age of the
02:59:34 computer industry. And it’s I mean, I think it’s cool that we can still run, you know,
02:59:39 Mathematica version one programs today and so on. And we’ve sort of maintained compatibility.
02:59:44 And we’ve been just building this big tower all those years of just more and more and more
02:59:49 computational capabilities. It’s sort of interesting. We just made this this picture
02:59:54 of kind of the different kind of threads of of of computational content, of, you know,
02:59:59 mathematical content and and, you know, all sorts of things with, you know, data and graphs and
03:00:05 whatever else. And what you see in this picture is about the first 10 years. It’s kind of like
03:00:10 it’s just a few threads. And then then about maybe 15, 20 years ago, it kind of explodes
03:00:16 in this whole collection, different threads of all these different capabilities that are now
03:00:20 part of open language and representing different things in the world. But the thing that was super
03:00:25 lucky in some sense is it’s all based on one idea. It’s all based on the idea of symbolic expressions
03:00:31 and transformation rules for symbolic expressions, which was kind of what I originally
03:00:36 put into this SMP system back in 1979 that was a predecessor of the whole open language stack.
03:00:42 So that idea was an idea that I got from sort of trying to understand mathematical logic and so on.
03:00:48 It was my attempt to kind of make a general human comprehensible model of computation
03:00:54 of just everything is a symbolic expression. And all you do is transform symbolic expressions.
03:01:00 And, you know, in in retrospect, I was very lucky that I understood as little as I understood then,
03:01:06 because had I understood more, I would have been completely freaked out about all the different
03:01:11 ways that that kind of model can can fail. Because what do you do when you have a symbolic
03:01:17 expression, you make transformations for symbolic expressions? Well, for example, one question is,
03:01:22 there may be many transformations that could be made in a very multi computational kind of way.
03:01:26 But what we’re doing is picking, we’re using the first transformation
03:01:30 that applies. And we keep doing that until we reach a fixed point. And that’s the result. And
03:01:35 that’s kind of a very, it’s kind of a way of sort of sliding around the edge of multi computation.
03:01:42 And back when I was working on SMP and things, I actually thought about these questions about
03:01:46 about how, you know, how, what determines the this kind of evaluation path. So for example,
03:01:52 you know, you work out Fibonacci, you know, Fibonacci is a recursive thing, f of n is f of
03:01:57 n minus one plus f of n minus two, and you get this whole tree of recursion, right? And there’s
03:02:02 the question of how do you evaluate that tree of recursion? Do you do it sort of depth first,
03:02:06 where you go all the way down one side? Do you do it breadth first, where you’re kind of collecting
03:02:10 the terms together, where you know that, you know, f of eight plus f of seven, f of seven,
03:02:14 plus f of six, you can collect the f of sevens, and so on. These are, you know, I didn’t realize
03:02:20 that at the time, it’s kind of funny, I was working on on gauge field theories back in 1979.
03:02:25 And I was also working on the evaluation model in SMP. And they’re the same problem. But it took me
03:02:31 40 more years to realize that. And this question about how you do this sort of evaluation front,
03:02:37 that’s a question of reference frames. It’s a question of kind of the story of I mean,
03:02:42 that that’s, that is basically this question of, in what order is the universe evaluated?
03:02:48 And that’s, and so what you realize is, there’s this whole sort of world of different kinds of
03:02:52 computation that you can do, sort of multi computationally. And that’s a, that’s an
03:02:57 interesting thing. It has a lot of implications for distributed computing, and so on. It also has
03:03:01 a potential implication for blockchain, which we haven’t fully worked out, which is, and this is
03:03:06 not what we’re doing with Cardano, but but this is a different thing. The this is something where
03:03:13 one of the questions is, when you have, in a sense, blockchain is a deeply sequentialized
03:03:19 story of time. Because in blockchain, there’s just one copy of the ledger. And you’re saying,
03:03:26 this is what happened, you know, time has progressed in this way. And there are little
03:03:29 things around the edges, as you try and reach consensus and so on. And, and, you know, actually,
03:03:34 we just recently, we’ve had this little conference we organized about the theory of distributed
03:03:39 consensus, because I realized that a bunch of interesting things that some of our science can
03:03:44 tell one about that. But that’s a different let’s let’s not go down that that part. Yeah,
03:03:48 but distributed consensus that still has a sequential there’s like, there’s still
03:03:51 sequentiality. So don’t tell me you’re thinking through like how to apply multi computation to
03:03:57 blockchain. Yes. And so so that becomes a story of, you know, instead of transactions all having
03:04:04 to settle in one ledger, it’s like a story of all these different ledgers. And they all have to have
03:04:10 some ultimate consistency, which is what causal invariance would give one, but it can take a
03:04:15 while. And the it can take a while is kind of like quantum mechanics. So it’s kind of what’s
03:04:19 happening is there these different paths of history that correspond to, you know, in one path
03:04:25 of history, you got paid this amount in another path of history, you got paid this amount. In the
03:04:29 end, the universe will always become consistent. Now, now the way it will it works is, okay, it’s
03:04:36 a little bit more complicated than that. What happens is, the way space is knitted together
03:04:40 in our theory of physics is through all these events. And the the idea is that the way that
03:04:47 economic space is knitted together is between is there these autonomous events that essentially
03:04:52 knit together economic space. So there are all these threads of transactions that are happening.
03:04:57 And the question is, can they be made consistent? Are there is there something forcing them to be
03:05:01 sort of a consistent fabric of economic reality? And sort of what this has led me to is trying to
03:05:08 realize how does economics fundamentally work? And, you know, what is economics? And, you know,
03:05:14 what what are the atoms of economics, so to speak? And so what I’ve kind of realized is that, that
03:05:20 sort of the perhaps I don’t even know if this is right yet, there’s sort of events in economics,
03:05:25 the transactions, there are states of agents that are kind of the atoms of economics. And then
03:05:32 transactions are kind of agents transact in some transact in some way, and that’s an event. And
03:05:38 then the question is, how do you knit together sort of economic space from that? What is there
03:05:43 in economic space? Well, all these transactions, there’s a whole complicated collection of possible
03:05:48 transactions. But one thing that’s true about economics is we tend to have the notion of a
03:05:52 definite value for things. We could imagine that, you know, you buy a cookie from somebody, and
03:06:02 they want to get a movie ticket. And there is some way that AI bots could make some path
03:06:09 from the cookie to the movie ticket by all these different intermediate transactions. But in fact,
03:06:16 we have an approximation to that, which is we say they each have a dollar value. And we have this
03:06:21 kind of numeraire concept of there’s just a way of kind of taking this whole complicated space of
03:06:28 transactions and parsing it in something which is a kind of a simplified thing that is kind of like
03:06:34 our parsing of physical space. And so my guess is that the yet again, I mean, it’s crazy that all
03:06:41 these things are so connected. This is another multi computation story. Another story of where
03:06:48 what’s happening is that the economic consciousness, the economic observer is not going to deal with
03:06:54 all of those are different microscopic transactions. They’re just going to parse the
03:06:57 whole thing by saying, there’s this value, it’s a number. And that’s their understanding of their
03:07:03 summary of this economic network. And there will be all kinds of things like there are all kinds of
03:07:07 arbitrage opportunities, which are kind of like the quantum effects in this whole thing. And that’s
03:07:14 in places where there’s sort of different paths that can be followed and so on. So the question
03:07:21 is, can one make a sort of global theory of economics? And then my test case is again,
03:07:27 what is time dilation in economics? And I know if you imagine a very agricultural economics where
03:07:33 people are growing lettuces and fields and things like this, and you ask questions about, well,
03:07:38 if you’re transporting lettuces to different places, what is the value of the lettuces after
03:07:43 you have to transport them versus if you’re just sitting in one place and selling them,
03:07:47 you can kind of get a little bit of an analogy there. But I think there’s a better and more
03:07:51 complete analogy. And that’s the question of, is there a theory like general relativity that is a
03:07:56 global theory of economics? And is it about something we care about? It could be that there
03:08:00 is a global theory, but it’s about a feature of economic reality that isn’t important to us.
03:08:05 Now, another part of the story is, can one use those ideas to make essentially a distributed
03:08:11 blockchain, a distributed generalization of blockchain, kind of the quantum analog of money,
03:08:16 so to speak, where you have, for example, you can have uncertainty relations where you’re saying,
03:08:21 you know, well, if I insist on knowing my bank account right now, there’ll be some uncertainty.
03:08:27 If I’m prepared to wait a while, then it’ll be much more certain. And so there’s, you know,
03:08:32 is there a way of using and so we’ve made a bunch of prototypes of this, which I’m not yet happy
03:08:39 with. But what I realized is, to really understand these prototypes, I actually have to have a
03:08:43 foundational theory of economics. And so that’s kind of a, you know, it may be that we could
03:08:48 deploy one of these prototypes as a practical system. But I think it’s really going to be much
03:08:52 better if we actually have an understanding of how this plugs into kind of the economics.
03:08:56 And that means like a fundamental theory of transactions between
03:09:00 entities. That’s what you mean by economics.
03:09:03 Yes, I think so. But I mean, you know, how there emerge sort of laws of economics,
03:09:08 I don’t even know. And I’ve been asking friends of mine who are economists and things,
03:09:12 what is economics? You know, is it an axiomatic theory? Is it a theory
03:09:17 that is kind of a qualitative description theory? Is it, you know, what kind of a theory is it? Is
03:09:22 it a theory, you know, what kind of thinking? It’s like in biology, in evolutionary biology,
03:09:27 for example, there’s a certain pattern of thinking that goes on in evolutionary biology where
03:09:32 if you’re a, you know, a good evolutionary biologist, somebody says, that creature has a
03:09:36 weird horn. And they’ll say, well, that’s because this and this and this and the selection of this
03:09:41 kind and that kind. And that’s the story. And it’s not a mathematical story. It’s a story of
03:09:46 a different type of thinking about these things. By the way, evolutionary biology is yet another
03:09:52 place where it looks like this multi computational idea can be applied. And that’s where maybe
03:09:58 speciation is related to things like event horizons. And there’s a whole other kind of
03:10:03 world of that. But it seems like this kind of model can be applicable to so many aspects,
03:10:09 like the different levels of understanding of our reality. So it could be the biology,
03:10:15 the chemistry, at the physics level, the economics. And you could potentially, the thing is, it’s like,
03:10:24 okay, sure, at all these levels, it might rhyme. It might make sense as a model. The question is,
03:10:28 can you make useful predictions as one of these levels? That’s right. And that’s really a question
03:10:34 of, you know, it’s a weird situation because the situation where the model probably has definite
03:10:40 consequences. The question is, are they consequences we care about? Yeah. And that’s
03:10:45 some, you know, and so in the case of, in the economic case, the, where, so, you know,
03:10:55 one thing is this idea of using kind of physics like notions to construct a kind of distributed
03:11:02 analog of blockchain. Okay. The much more pragmatic thing is a different direction.
03:11:07 And it has to do with this computational language that we built to describe the world
03:11:11 that knows about, you know, different kinds of cookies and knows about different cities and
03:11:15 knows about how to compute all these kinds of things. One of the things that is of interest is
03:11:21 if you want to run the world, you need, you know, with contracts and laws and rules and so on,
03:11:27 there are rules at a human level and there are kind of things like, and so this gets one into
03:11:33 the idea of computational contracts. You know, right now when we write a contract, it’s a piece
03:11:38 of legalese. It’s, you know, it’s just written in English and it’s not something that’s automatically
03:11:43 analyzable, executable, whatever else. It’s just English. You know, back in Gottfried Leibniz,
03:11:50 back in, you know, 1680 or whatever was like, I’m going to, you know, figure out how to use logic
03:11:57 to decide legal cases and so on. And he had kind of this idea of let’s make a computational language
03:12:02 for the human law. Forget about modeling nature, forgot about natural laws. What about human law?
03:12:09 Can we make kind of a computational representation of that? Well, I think finally we’re close to
03:12:14 being able to do that. And one of the projects that I hope to get to as soon as there’s a little
03:12:20 bit of slowing down of some of this Cambrian explosion that’s happening is a project I’ve
03:12:24 been meaning to really do for a long time, which is what I’m calling a symbolic discourse language.
03:12:29 It’s just finishing the job of being able to represent everything like the conversation we’re
03:12:34 having in computational terms. And one of the use cases for that is computational contracts.
03:12:40 Another use case is something like the constitution that says what the AIs, what we want the AIs to do.
03:12:45 So, but this is useful. So you’re saying, so these are like, you’re saying computational contracts,
03:12:50 but smart contracts. This is what’s in the domain of cryptocurrency is known as smart contracts.
03:12:55 And so the language you’ve developed, this symbolic or seek to further develop symbolic discourse
03:13:02 language enables you to write a contract and write a contract that richly represents
03:13:10 some aspect of the world. So, I mean, smart contracts tend to be right now mostly about
03:13:16 things happening on the blockchain. And sometimes they have oracles. And in fact, our Wolfman Alpha
03:13:20 API is the main thing people use to get information about the real world, so to speak,
03:13:26 within smart contracts. So Wolfram Alpha, as it stands, is a really good oracle for
03:13:31 whoever wants to use it. That’s perhaps where the relationship with Cardano is.
03:13:34 Yeah, well, that’s how we started getting involved with blockchains. As we realized,
03:13:37 people were using Wolfram Alpha as the oracle for smart contracts, so to speak. And so that
03:13:43 got us interested in blockchains in general. And what was ended up happening is Wolfram Language
03:13:49 is, with its symbolic representation of things, is really very good at representing things like
03:13:53 blockchains. And so I think we now have, and we don’t really know all the comparisons, but we now
03:13:58 have a really nice environment within Wolfram Language for dealing with the sort of, for
03:14:04 representing what happens in blockchains, for analyzing what happens in blockchains.
03:14:08 We have a whole effort in blockchain analytics. And we’ve sort of published some samples of how
03:14:15 that works. But it’s because our technology stack, Wolfram Language and Mathematica,
03:14:20 are very widely used in the quant finance world. There’s a sort of immediate coevolution there of
03:14:29 the quant finance kind of thing and blockchain analytics. So it’s kind of the representation
03:14:35 of blockchain in computational language. Then ultimately, it’s kind of like, how do you run
03:14:40 the world with code? That is, how do you write sort of all these things which are right now,
03:14:45 regulations and laws and contracts and things in computational language? And kind of the ultimate
03:14:50 vision is that sort of something happens in the world, and then there’s this giant domino effect
03:14:55 of all these computational contracts that trigger based on the thing that happened. And there’s a
03:15:00 whole story to that. And of course, I like to always pay attention to the latest things that
03:15:06 are going on. And I really, I kind of like blockchain because it’s another rethinking
03:15:11 of kind of computation. It’s kind of like cloud computing was a little bit of that, of sort of
03:15:16 persistent kind of computational resources and so on. And this multi computation is a big
03:15:23 rethinking of kind of what it means to compute. Blockchain is another bit of rethinking of what
03:15:28 it means to compute. The idea that you lodge kind of these autonomous lumps of computation
03:15:33 out there in the blockchain world. And one of the things that just sort of for fun,
03:15:39 so to speak, is we’ve been doing a bit of stuff with NFTs, and we just did some NFTs on Cardano,
03:15:44 and we’ll be doing some more. And we did some cellular automaton NFTs on Cardano,
03:15:48 which people seem to like quite a bit. And one of the things I’ve realized about NFTs
03:15:55 is that there’s kind of this notion, and we’re really working on this, I like recording stuff.
03:16:01 You know, one of the things that’s come out of kind of my science, I suppose, is this history
03:16:06 matters type story of, you know, it’s not just the current state, it’s the history that matters.
03:16:11 And I’ve kind of, I don’t think this is actually realizing, maybe it’s not coincidental that I’m
03:16:17 sort of the human who’s recorded more about themselves than anybody else. And then I end up
03:16:20 with these science results that say history matters, which was not those things. I didn’t
03:16:26 think those were connected, but they’re at least correlated, yes. Yeah, right. So, you know,
03:16:30 this question about sort of recording what has happened and having sort of a permanent record
03:16:36 of things, one of the things that’s kind of interesting there is, you know, you put up a
03:16:39 website and it’s got a bunch of stuff on it, but you know, you have to keep paying the hosting
03:16:43 fees or the thing’s going to go away. But one of the things about blockchain is quite interesting
03:16:48 is if you put something on a blockchain and you pay, you know, your commission to get that thing,
03:16:53 you know, put on, you know, mine, put on the blockchain, then in a sense, everybody who comes
03:16:59 after you is, you know, they are motivated to keep your thing alive because that’s what keeps
03:17:04 the consistency of the blockchain. So in a sense with sort of the NFT world, it’s kind of like if
03:17:09 you want to have something permanent, well, at least for the life of the blockchain, but even if
03:17:14 the blockchain goes out of circulation, so to speak, there’s going to be enough value in that
03:17:18 whole collection of transactions that people are going to archive the thing. But that means that,
03:17:23 you know, pay once and you’re kind of, you’re lodged in the blockchain forever. And so we’ve
03:17:28 been kind of playing around with sort of a hobby thing of mine of thinking about sort of the NFTs
03:17:35 and how you and sort of the consumer idea of kind of the it’s the it’s the anti, you know,
03:17:41 it’s the opposite of the Snapchat view of the world. There’s a permanence to it that’s heavily
03:17:46 incentivized and thereby you can have a permanence of history. Right. And that’s that’s that’s kind of
03:17:54 the now, you know, so that’s so that’s one of the things we’ve been doing with Cardano. And it’s
03:17:59 kind of fun. I think that I mean, this whole question about, you know, you mentioned automated
03:18:03 theorem proving and blockchains and so on. And as I’ve thought about this kind of physics inspired
03:18:08 distributed blockchain, obviously, there, the sort of the proof that it works, that there are no
03:18:14 double spends, there’s no whatever else, that proof becomes a very formal kind of almost a
03:18:20 matter of physics, so to speak. And, you know, it’s been it’s been an interesting thing for the
03:18:25 for the practical blockchains to do kind of actual automated theorem proving. And I don’t think
03:18:30 anybody’s really managed it in an interesting case yet. It’s a thing that people, you know,
03:18:34 aspire to. But I think it’s a challenging thing because basically, the point is one of the one
03:18:39 of the things about proving correctness of something as well. You know, people say I’ve
03:18:44 got this program and I’m going to prove it’s correct. It’s like, what does that mean? You
03:18:47 have to say what correct means. I mean, it’s it’s kind of like then you have to have another
03:18:51 language. And people are very confused back in past decades of, you know, oh, we’re going to
03:18:56 prove the correctness by representing the program in another language, which we also don’t know
03:19:00 whether it’s correct. And, you know, often by correctness, we just mean it can’t crash or it
03:19:06 can’t scribble on memory. But but the thing is that there’s this complicated trade off,
03:19:10 because as soon as there’s as soon as you’re really using computation, you have computational
03:19:15 irreducibility, you have undecidability. If you want to use computation seriously,
03:19:20 you have to kind of let go of the idea that you’re going to be able to box it in and say,
03:19:26 we’re going to have just this happen and not anything else. I mean, this is a this is an old
03:19:30 fact. I mean, Gödel’s theorem tries to say, you know, piano arithmetic, the axioms of arithmetic,
03:19:35 can you box in the integers and say these axioms give just the integers and nothing about the
03:19:40 integers. Gödel’s theorem showed that wasn’t the case. You can have all these wild, weird things
03:19:46 that are obey the piano axioms, but aren’t integers. And there’s this kind of infinite
03:19:50 hierarchy of additional axioms you would have to add. And it’s kind of the same thing. You don’t
03:19:55 get to, you know, if you want to say, I want to know what happens, you’re boxing yourself in and
03:20:00 there’s a limit to what can happen, so to speak. So it’s a complicated trade off. And it’s a big
03:20:05 trade off for AI, so to speak. It’s kind of like, do you want to let computation actually do what
03:20:09 it can do? Or do you want to say, no, it’s very, very boxed in to the point where we can understand
03:20:14 every step. And that’s kind of a thing that becomes difficult to do. But that’s, I mean,
03:20:21 in general, I would say one of the things that’s kind of complicated in my sort of life and the
03:20:28 whole sort of story of computational language and all this technology and science and so on.
03:20:32 I mean, I kind of in the flow of one’s life, it’s sort of interesting to see how these things play
03:20:38 out because I’ve kind of concluded that I’m in the business of making kind of artifacts from the
03:20:43 future, which means, you know, there are things that I’ve done, I don’t know, this physics project,
03:20:48 I don’t know whether anybody would have gotten to it for 50 years. You know, the fact that
03:20:52 Mathematica is a third of a century old, and I know that a bunch of the core ideas are not
03:20:58 well absorbed. I mean, that is people finally got this idea that I thought was a triviality
03:21:02 of notebooks, that was 25 years. And, you know, some of these core ideas about symbolic computation
03:21:08 and so on are not absorbed. I mean, people use them every day in Wolfram language and, you know,
03:21:15 do all kinds of cool things with them. But if you say, what is the fundamental intellectual point
03:21:19 here? It’s not well absorbed. And it’s something where you kind of realize that you’re sort of
03:21:25 building things. And I kind of made this thing about, you know, we’re building artifacts from
03:21:30 the future, so to speak. And I mentioned that we have a conference coming up actually in a couple
03:21:35 of weeks, our annual technology conference, where we talk about all the things we’re doing.
03:21:41 And, you know, so I was talking about it last year, about, you know, we’re making artifacts
03:21:46 from the future. And I was kind of like, I had some version of that, that was kind of a dark
03:21:50 and frustrated thing of like, you know, I’m building things which nobody’s going to care
03:21:54 about until long after I’m dead, so to speak. But then I realized, you know, people were sort of
03:22:01 telling me afterwards, you know, that’s exactly how, you know, we’re using Wolfram language in
03:22:06 some particular setting and, you know, some computational X field or some organization or
03:22:10 whatever. And it’s like, people are saying, oh, you know, what did you manage to do? You know,
03:22:15 well, we know that in principle, it will be possible to do that. But we didn’t know that
03:22:18 was possible now. And it’s kind of like, that’s sort of the business we’re in. And in a sense,
03:22:23 with some of these ideas in science, you know, I feel a little bit the same way that there are
03:22:27 some of these things where, you know, some things like, for example, this whole idea, well, so to
03:22:35 relate to another sort of piece of history and the future, one of, you know, I mentioned at the
03:22:39 beginning kind of complexity as this thing that I was interested in back 40 years ago and so on.
03:22:44 Where does complexity come from? Well, I think we kind of nailed that. The answer is in the
03:22:50 computational universe, even simple programs make it. And that’s kind of the secret that nature has
03:22:54 that allows you to make it. So that’s that part. But the bigger picture there was this idea of
03:23:02 this kind of computational paradigm, the idea that you could go beyond mathematical equations,
03:23:06 which have been sort of the primary modeling medium for 300 years. And so it was like, look,
03:23:13 it is inexorably the case that people will use programs rather than just equations. And, you
03:23:18 know, I was saying that in the 1980s and people were, you know, I published my big book, New Kind
03:23:22 of Science, that’ll be 20 years ago next year. So in 2002, and people were saying, oh, no,
03:23:28 this can’t possibly be true. You know, we know for 300 years we’ve been doing all this stuff.
03:23:32 Right. To be fair, I now realize I’m a little bit more analysis of what people actually
03:23:38 said in pretty much every field other than physics. People said, oh, these are new models.
03:23:44 That’s pretty interesting. In physics, people were like, we’ve got our physics models. We’re
03:23:48 very happy with them. Yeah, in physics, there’s more resistance because of the attachment and
03:23:53 the power of the equations. The idea that programs might be the right way to approach
03:23:59 this field. Was there some resistance? And like you’re saying, it takes time. For somebody who
03:24:05 likes the idea of time dilation and all these applications, I thought you would understand this.
03:24:09 Yeah, right. But, you know, and computational irreducibility. Yes, exactly. But I mean,
03:24:14 it is really interesting that just 20 years, a span of 20 years, it’s gone from, you know,
03:24:20 pitchforks and horror to, yeah, we get it. And, you know, it’s helped that we’ve, you know, in our
03:24:28 current effort in fundamental physics, we’ve gotten a lot further and we’ve managed to
03:24:33 put a lot of puzzle pieces together that make sense. But the thing that I’ve been thinking
03:24:37 about recently is this field of complexity. So I’ve kind of was a sort of a field builder.
03:24:43 Back in the 1980s, I was kind of like, okay, you know, can we, you know, I’d understood this point
03:24:50 that there was this sort of fundamental phenomenon of complexity that showed up in lots of places.
03:24:54 And I was like, this is an interesting sort of field of science. And I was recently was reminded,
03:25:01 I was at this, the very first sort of get together of what became the Santa Fe Institute. And I was
03:25:07 like, in fact, there’s even an audio recording of me sort of saying, people have been talking about,
03:25:11 oh, what should this, you know, outfit do? And I was saying, well, there is this thing that I’ve
03:25:16 been thinking about. It’s this kind of idea of complexity. And it’s kind of like, and that’s
03:25:21 what that ended up. And you planted the seed of complexity at Santa Fe. That’s beautiful.
03:25:25 It’s a beautiful vision. But I mean, so that, but what’s happened then is this idea of complexity
03:25:31 and, you know, and I started the first research center at University of Illinois for doing that
03:25:35 in the first journal, complex systems and so on. And it’s kind of an interesting thing in my life,
03:25:42 at least that it’s kind of like you plant the seed, you have this idea. It’s a kind of a science
03:25:47 idea. You have this idea of sort of focusing on the phenomenon of complexity. The deeper idea was
03:25:52 this computational paradigm. But the nominal idea is this kind of idea of complexity. Okay. Then you
03:25:58 roll time forward 30 years or whatever, 35 years, whatever it is. And you say, what happened? Okay.
03:26:05 Well now there are a thousand complexity institutes around the world. I think more or less,
03:26:10 we’ve been trying to count them. And, you know, there are 40 complexity journals, I think.
03:26:16 And so it’s kind of like what actually happened in this field, right? And I look at a lot of what
03:26:22 happened and I’m like, you know, I have to admit to some eye rolling, so to speak, because it’s
03:26:28 kind of like, like, what is, what’s actually going on? Well, what people definitely got
03:26:33 was this idea of computational models. And then they got, but they thought one of the,
03:26:38 one of the kind of cognitive mistakes, I think is they say, we’ve got a computational model
03:26:43 and it, and we’re looking at a system that’s complex and our computational model gives
03:26:49 complexity. By golly, that must mean it’s right. And unfortunately, because complexity is a generic
03:26:55 phenomenon and computational irreducibility is a generic phenomenon that actually tells you nothing.
03:27:01 And so then the question is, well, what can you do? You know, there’s a lot of things that have
03:27:06 been sort of done under this banner of complexity. And I think it’s been very successful in providing
03:27:10 sort of an interdisciplinary way of connecting different fields together. Which is powerful
03:27:15 in itself. Right. I mean, that’s a very useful. Biology and economics and physics. Right. It’s a
03:27:19 good organizing principle, but in the end, a lot of that is around this sort of computational
03:27:23 paradigm, computational modeling. That’s the raw material that powers that kind of, that kind of
03:27:28 correspondence, I think. But the question is sort of, what is the, you know, I was just thinking
03:27:33 recently, you know, we’ve been, I mean, the other we’ve been, we’ve been for years, people have
03:27:38 told me you should start some Wolfram Institute that does basic science. You know, all I have
03:27:43 is a company that, that builds software and we, you know, we have a little piece that does basic
03:27:47 science as kind of a hobby. People are saying you should start this Wolfram Institute thing.
03:27:52 And I’ve been, you know, cause I’ve known about lots of institutes and I’ve seen kind of their
03:27:56 flow of money and, and kind of, you know, what happens in different situations and so on. So I’ve
03:28:00 been kind of reluctant, but, but I’ve, I’ve, I have realized that, you know, what we’ve done with
03:28:05 our company over the last 35 years, you know, we built a very good machine for doing R and D and,
03:28:10 you know, innovating and creating things. And I just applied that machine to the physics project.
03:28:16 That’s how we did the physics project in a fairly short amount of time with a, you know,
03:28:20 a efficient machine with, you know, various people involved and so on. And so, you know,
03:28:25 it, it works for basic science and it’s like, we can do more of this. And so now.
03:28:31 In biology and chemistry, so it’s, it’s become an institute.
03:28:34 Yes. Well, it needs to become an institute.
03:28:36 An official institute.
03:28:37 Right. Right. But the, the thing that, so I was thinking about, okay, so what do we do with
03:28:41 complexity? You know, what, what, there are all these people who’ve, you know, what, what should
03:28:46 happen to that field? And what I realized is there’s kind of this area of foundations of
03:28:50 complexity. That’s about these questions about simple programs, what they do that’s far away
03:28:56 from a bunch of the detailed applications that people, it’s not far away. It’s, it’s the,
03:29:00 it’s the under, you know, the, the bedrock underneath those applications. And so I realized
03:29:05 recently, this is my recent kind of little innovation of a sort, a post that I’ll do very
03:29:12 soon about kind of, you know, the foundations of complexity. What really are they? I think
03:29:20 there are really two ideas, two conceptual ideas that I hadn’t really enunciated, I think before.
03:29:26 One is what I call meta modeling. The other is ruleology. So what is meta modeling? So
03:29:31 meta modeling is you’ve got this complicated model and it’s a model of, you know, hedgehogs
03:29:36 interacting with this, interacting with that. And the question is what’s really underneath that?
03:29:40 What is it? You know, is it a Turing machine? Is it a cellular automaton? You know,
03:29:45 what is the underlying stuff underneath that model? And so there’s this kind of meta science
03:29:51 question of given these models, what is the core model? And I realized, I mean, to me,
03:29:56 that’s sort of an obvious question, but then I realized I’ve been doing language design for 40
03:30:00 years and language design is exactly that question. You know, underneath all of this
03:30:05 detailed stuff people do, what are the underlying primitives? And that’s a question people haven’t
03:30:10 tended to ask about models. They say, well, we’ve got this nice model for this and that and the
03:30:13 other, what’s really underneath it? And what, you know, because once you have the thing that’s
03:30:18 underneath it, well, for example, this multi computation idea is an ultimate meta modeling
03:30:24 idea because it’s saying underneath all these fields is one kind of paradigmatic structure.
03:30:29 And, you know, you can imagine the same kind of thing in much more sort of much sort of shallower
03:30:36 levels in different kinds of modeling. So the first activity is this kind of meta modeling,
03:30:41 the kind of the models about models, so to speak. You know, what is the, what’s, you know,
03:30:47 drilling down into models? That’s one thing. The other thing is this thing that I think we’re
03:30:53 going to call ruleology, which is kind of the, okay, you’ve got these simple rules. You’ve got
03:30:57 cellular automata, you’ve got turing machines, you’ve got substitution systems, you’ve got
03:31:01 register machines, you’ve got all these different things. What do they actually do in the wild? And
03:31:06 this is an area that I’ve spent a lot of time, you know, working on. It’s a lot of stuff in my new
03:31:10 kind of science book is about this. You know, this new book I wrote about combinators is full of
03:31:16 stuff like this. And this journal Complex Systems has lots of papers about these kinds of things.
03:31:21 But there isn’t really a home for people who do ruleology or what I’m now…
03:31:26 As you call the basic science of rules.
03:31:29 Yes. Yes. Right. So it’s like, you’ve got some, what is it? Is it mathematics? No,
03:31:35 it isn’t really like mathematics. In fact, from my now understanding of metamathematics,
03:31:38 I understand that it’s the molecular dynamics level. It’s not the level that mathematicians
03:31:43 have traditionally cared about. It’s not computer science because computer science is about writing
03:31:48 programs that do things, you know, that were for a purpose, not programs in the wild, so to speak.
03:31:53 It’s not physics. It doesn’t have anything to do with, you know, maybe underneath some physics,
03:31:57 but it’s not physics as such. So it just hasn’t had a home. And if you look at, you know,
03:32:02 but what’s great about it is it’s a surviving field, so to speak. It’s something where,
03:32:08 you know, one of the things I find sort of inspiring about mathematics, for example,
03:32:13 is you look at mathematics that was done, you know, in ancient Greece, ancient, you know, Babylon,
03:32:18 Egypt, and so on. It’s still here today. You know, you find an icosahedron that somebody made
03:32:23 in ancient Egypt. You look at it. Oh, that’s a very modern thing. It’s an icosahedron. You know,
03:32:28 it’s a timeless kind of activity. And this idea of studying simple rules and what they do,
03:32:34 it’s a timeless activity. And I can see that over the last 40 years or so as, you know,
03:32:39 even with cellular automata, it’s kind of like, you know, you can sort of catalog what are the
03:32:44 different cellular automata used for and, you know, like the simplest rules like one, you might
03:32:50 even know this one, Rule 184. Rule 184 is a minimal model for road traffic flow. And, you know, it’s
03:32:56 also a minimal model for various other things. But it’s kind of fun that you can literally say,
03:33:01 you know, Rule 90 is a minimal model for this and this and this. Rule 4 is a minimal model for this.
03:33:07 And it’s kind of remarkable that you can just by in this raw level of this kind of study of rules,
03:33:13 they then branch, they’re the raw material that you can use to make models of different things.
03:33:17 So it’s a very pure basic science, but it’s one that, you know, people have explored it,
03:33:23 but they’ve been kind of a little bit in the wilderness. And I think, you know, one of the
03:33:27 things that I would like to do finally is, you know, I always thought that sort of this notion
03:33:32 of pure NKS, pure NKS being the acronym for my book, New Kind of Science, was something that
03:33:40 people should be doing. And, you know, we tried to figure out what’s the right institutional
03:33:44 structure to do this stuff. You know, we dealt with a bunch of universities. Oh, you know,
03:33:48 can we do this here? Well, what department would be in it? Well, it isn’t in a department. It’s
03:33:53 its own new kind of thing. That’s why the book was called The New Kind of Science.
03:33:58 It’s kind of the, because that’s an increasingly good description of what it is, so to speak.
03:34:03 We’re actually, we were thinking about kind of the ruleological society because we’re realizing
03:34:08 that it’s kind of, it’s, you know, it’s very interesting. I mean, I’ve never really done
03:34:14 something like this before because there’s this whole group of researchers who are,
03:34:18 who’ve been doing things that are really, in some cases, very elegant, very surviving, very solid,
03:34:24 you know, here’s this thing that happens in this very abstract system. But it’s like,
03:34:29 it’s like, what is that part of, you know, it doesn’t have a home. And I think that’s something
03:34:34 I, you know, I kind of fault myself for not having been more, you know, when complexity
03:34:38 was developing in the 80s, I didn’t understand the danger of applications. That is, it’s really
03:34:46 cool that you can apply this to economics and you can apply it to evolutionary biology and this and
03:34:50 that and the other. But what happens with applications is everything gets sucked into
03:34:54 the applications. And the pure stuff, it’s like the pure mathematics, there isn’t any pure
03:34:59 mathematics, so to speak. It’s all just applications of mathematics. And I failed to kind of make sure
03:35:05 that this kind of pure area was kind of maintained and developed. And I think now, you know, one of
03:35:12 the things I want to try to do and, you know, it’s a funny thing because I’m used to, look,
03:35:17 I’ve been a tech CEO for more than half my life now. So, you know, this is what I know how to do.
03:35:22 And, you know, I can make stuff happen and get projects to happen, even as it turns out,
03:35:28 basic science projects in that kind of setting and how that translates into kind of, you know,
03:35:34 there are a lot of people working on, for example, our physics project sort of distributed through
03:35:38 the academic world and that’s working just great. But the question is, you know, can we have a sort
03:35:42 of accelerator mechanism that makes use of kind of what we’ve learned in sort of R&D innovation?
03:35:49 And, you know, but on the other hand, it’s a funny thing because, you know, in a company,
03:35:54 in the end, the thing is, you know, it’s a company, it makes products, it sells things,
03:35:58 sells things to people. And, you know, when you’re doing basic research, one of the challenges is
03:36:03 there isn’t that same kind of sort of mechanism. And so it’s, you know, how do you drive the thing
03:36:09 in a kind of, in a led kind of way so that it really can make forward progress rather than,
03:36:16 you know, what can often happen in, you know, in academic settings where it’s like,
03:36:20 well, there are all these flowers blooming, but it’s not clear that, you know, that it’s…
03:36:24 You have to have a central mission and a drive, just like you do with a company that’s delivering
03:36:29 a big overarching product. And that’s… But the challenge is, you know, when you have
03:36:35 the economics of the world are such that, you know, when you’re delivering a product and people
03:36:40 say, wow, that’s useful, we’ll buy it. And then that kind of feeds back and, okay, then you can
03:36:45 pay the people who build it to eat, you know, so they can eat and so on. And with basic science,
03:36:52 the payoff is very much less visible. And, you know, with this physics project, as I say,
03:36:57 the big surprise has been that, I mean, you know, for example, well, the big surprise with
03:37:02 the physics project is that it looks like it has near term applications. And I was like,
03:37:07 I’m guessing this is 200 years away. I was kind of using the analogy of, you know, Newton
03:37:14 starting a satellite launch company, which would have been kind of wrong time.
03:37:19 And, you know, but it turns out that’s not the case, but we can’t guarantee that. And if you say
03:37:24 we’re signing up to do basic research, basic rheology, let’s say, and, you know, and we can’t,
03:37:31 we don’t know the horizon, you know, it’s an unknown horizon. It’s kind of like an undecidable
03:37:36 kind of proposition of when is this proof going to end, so to speak? When is it going to be
03:37:40 something that gets applied? Well, I hope this becomes a vibrant new field of rheology. I love
03:37:48 it. Like I told you many, many times, it’s one of the most amazing ideas that has been brought to
03:37:55 this world. So I hope you get a bunch of people to explore this world. Thank you once again for
03:38:03 spending your really valuable time with me today. Fun stuff. Thank you. Thanks for listening to this
03:38:09 conversation with Stephen Wolfram. To support this podcast, please check out our sponsors in the
03:38:14 description. And now, let me leave you with some words from Richard Feynman. Nature uses only the
03:38:21 longest threads to weave her patterns, so each small piece of her fabric reveals the organization
03:38:28 of the entire tapestry. Thank you for listening and hope to see you next time.